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李进开

2018-08-28 11:54:13 来源:华南师范大学华南数学应用与交叉研究中心 点击: 收藏本文

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李进开(Jinkai LI)  教授


Email: jklimath@hotmail.com

研究方向:偏微分方程

 

PERSONAL INFORMATION

Date of Birth: November 20, 1984

Nationality: China

Address: South China Research Center for Applied Mathematics and  
                 Interdisciplinary Studies, South China Normal University,  
                 Zhong Shan Avenue West 55, Guangzhou 510631, China     

Email: jklimath@hotmail.com 


EDUCATIONS                                                                   

Aug 2010 – Jul 2013: Doctor of Philosophy, The Chinese University of Hong Kong  

                                Thesis title: Some Studies on the Hydrodynamical Models  of Nematic
                                                                     Liquid Crystals

                                      Thesis advisor:  Prof. Zhouping Xin

Aug 2006 -- Jul 2008: Master of Science, Jilin University, China

                                Thesis title: Existence of solutions for the p-Laplacian with critical  
                                                                     exponent and convection

                                      Thesis advisor: Prof. Jingxue Yin

Aug 2002 – Jul 2006: Bachelor of Science, Jilin University, P. R. China


PROFERSIONAL EXPERIENCES                                                                  

July 2018 – present:      Professor, South China Research Center for Applied Mathematics 
                                        and Interdisciplinary Studies, South China Normal University

Aug 2016  July 2018:  Research Assistant Professor, Department of Mathematics, The
                                        Chinese University of Hong Kong

Aug 3013 – July 2016: Postdoctoral Fellow, Department of Computer Science and
                                        Applied Mathematics, Weizmann Institute of Science
                                        (Mentor: Prof. Edriss S. Titi)  


RESEARCH INTERESTS

Global well-posedness to the geophysical dynamic flow such as the primitive equations, tropical atmosphere model with moisture, especially for the case with only partial viscosity or partial diffusivity.  

Well-posedness, stability, regularity and large-time behavior of solutions to the Cauchy or Dirichlet problem on fluid dynamic equations arising in mathematical physics, including

Navier-Stokes equations

Liquid Crystal equations

Boussinesq equations

Magnetohydrodynamics (MHD)

Existence, nonexistence, symmetry, regularity, local and global behavior of solutions to the Dirchlet problem of elliptic equations with Sobolev critical exponent or with variable exponent without variation structure.

RESEARCH GRANTS

1.   Sep 2017 -- Aug 2020: General Research Fund from RGC Hong Kong (PI, project no. 14302917), HK$ 473,351. Title: Weak and Strong Solutions to the Primitive Equations with Full or Horizontal Viscosity but No Diffusivity

2.   Jan. - Dec, 2017: Direct Grant 2016/2017 from CUHK (PI, Project Code: 4053216), HK$100,000. Title: Existence and Uniqueness of Solutions to Primitive Equations without Diffusivity


HONORS AND AWARDS

1. Israel Council for Higher Education (VATAT) Postdoctoral Fellowship

2. Best paper of Mathematical Models and Methods in Applied Sciences (M3AS)
   in 2016

3. 第二届中国科协优秀科技论文 2017

4. Simons Visiting Professor (SVP) to Oberwolfach


CONFERENCES AND WORKSHOPS

The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5--July 9, 2018 Taipei

2018 Conference on Nonlinear Partial Differential Equations Shenzhen University, Shenzhen, June 8--10, 2018

Conference on Mathematical Fluid Dynamics, May 7-11, 2018, Bad Boll, Germany

Conference on Mathematical Fluid Dynamics, May 7-11, 2018, Bad Boll, Germany

第五届偏微分方程青年学术论坛,厦门大学,4.20-232018

70/80偏微分方程青年学术论坛,四川大学,4.13--162018

Workshop on Compressible Navier-Stokes Systems and Related Problems (I)(II), 5-10 March 5-10 & 14-23, 2018, IMS, The Chinese University of Hong Kong, Hong Kong

IMS PDE Day (I) (II), Feb 2&7, 2018, Hong Kong

Nonlinear PDEs in Continuum Mechanics and Related Topics Workshop, Sanya, Hainan, Jan 22-26, 2018

10 26th Annual Meeting on Differential Equations and Related Topics, National Taiwan University, Taiwan, China, Jan 6-7, 2018

11 Recent Advances in Incompressible Flows, Capital Normal University, Beijing, China, Dec 8-10, 2017     

12 2017 Fall Program on Analysis of PDE -- (MHD and QG (week 12, Nov. 27-Dec.1), Conference on Analysis of Complex Fluids (week 10 Nov.13-Nov.17)), Boundary Layer problem and Liquid crystal (week 11, Nov. 20-Nov.24), Conference on Analysis of Classical Incompressible Fluids (week 5, Oct 9--13), Compressible Navier-Stokes Equations (week 3, Sep 25--29)), Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China

13 The 15th Summer School and Conference on Nonlinear Partial Differential Equations, Northwest University, Xi’an China.

14 Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations, (June 12 - 16, 2017, Wolfgang Pauli Institute (WPI), Vienna, Austria)

15 Darmstadt Analysis Day 2017 (May 16, 2017, Technische Universitat Darmstadt, Darmstadt, Germany)

16 Geophysical Fluid Dynamics (workshop ID 1719), (May 7 - 13, 2017, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany)

17 第四届偏微分方程青年学术论坛,(Mar 10 - 12, 2017, Guangzhou

18 Dynamics of Small Scales in Fluids, (February 13 - 17, 2017, ICERM, Brown University, Providence, USA)

19 IMS Workshop on PDEs (I), (Dec 29 - 31, 2016, IMS, The Chinese University of Hong Kong, Hong Kong)

20 International Conference on Evolution Equations, (May 16-20, 2016, Vanderbilt University, Nashville, TN, USA)

21 17th Mini-Workshop in Applied and Computational Mathematics, (Dec 28, 2015, Weizmann Institute of Science, Rehovot, Israel)

22 Workshop on Euler and Navier-Stokes Equations and Connected Topics, (Dec 14--18, 2015, Wolfgang Pauli Institute (WPI) , Vienna, Austria)

23 非线性扩散方程研讨会,(Nov 20--22, 2015, South China Normal University, Guangzhou

24 Mathematical Aspects of Hydrodynamics, (Aug 9--15, 2015, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany)

25 Workshop on Incompressible Fluids and the Applications, (Dalian Technology University, July 12 -- 14, 2015, Dalian, China)

26 Complex Analysis and Dynamical Systems VII, (May 10—15, 2015, Naharlya, Israel)

27 The Fifth Oklahoma PDE Workshop (February 28 -- March 1, 2015, Oklahoma State University, Stillwater, Oklahoma, USA)

28 2015 Joint Mathematics Meetings (January 10 -- 13, 2015, San Antonio, USA)

29 Informal Workshop on Euler, Navier-Stokes and Related Equations (January 8 -- 9, 2015, Texas A&M, College Station, USA)

30 The 16th Israeli Mini-Workshop in Applied and Computational Mathematics (December 30th, 2014, Technion, Haifa, Israel)

31 Fourth Workshop on Fluids and PDE (May 26 – 30, 2014, IMPA, Rio de Janeiro, Brazil)

32 Thematic Program on “Incompressible Fluid Dynamics” (May 07 – June 06, 2014, IMPA, Rio de Janeiro Brazil)

33 CMS summer school on "Microstructure: evolution and dynamics" (August 25 – 29, 2013, Technion, Haifa, Israel)

34 ICCM 2013 The Sixth International Congress of Chinese Mathematicians (July 14 – 19, 2013, Taipei)

35 International Conference on Analysis, Modeling and Computations of Complex Fluids (June 10 – 14, 2013, Zhejiang University, Hangzhou, China)

36 The Hong Kong Mathematical Society Annual General Meeting 2013 (June 8, 2013, The City University of Hong Kong, Hong Kong)

37 Hong Kong Mathematical Society Annual General Meeting 2012 (May 5, 2012, The University of Hong Kong, Hong Kong)

38 IMS Workshop on Partial Differential Equations (February 3 – 4, 2012, IMS CUHK, Hong Kong)

39 Recent Developments in Nonlinear Partial Differential Equations: Part II (May 15 – 21, 2011, IMS, CUHK, Hong Kong)

40 Recent Developments in Nonlinear Partial Differential Equations: Part I (February 28 – March 5, 2011, IMS, CUHK, Hong Kong)

41 ICCM 2010 The Firth International Congress of Chinese Mathematicians (December 18 – 22, 2010, Beijing, China)


TALKS AND SEMINARS

“Entropy-Bounded Solutions of the Compressible Navier-Stokes Equations with Vacuum” “Global Well-Posedness of the Anisotropic Primitive Equations” The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5--July 9, 2018 Taipei

“Some mathematical analysis on the dynamical models for atmosphere with moisture”, 2018 Conference on Nonlinear Partial Differential Equations Shenzhen University, Shenzhen, June 8--10, 2018

“Some mathematical analysis on the dynamical models for atmosphere with moisture”, Conference on Mathematical Fluid Dynamics, May 7-11, 2018, Bad Boll, Germany

“Entropy-bounded solutions of the full compressible Navier-Stokes equations with vacuum” 第五届偏微分方程青年学术论坛, Xiamen University, April 20--23, 2018

“Global well-posedness of the anisotropic primitive Equations”, 70/80偏微分方程青年学术论坛, Sichuan University, April 13 --16, 2018

Entropy-bounded solutions of the compressible Navier-Stokes equations with vacuum, Workshop on Compressible Navier-Stoke Systems and Related Problems (I), March 5--10, 2018, Hong Kong

“Entropy-bounded solutions of the compressible Navier-Stokes equations with far field vacuum” Nonlinear PDEs in Continuum Mechanics and Related Topics Workshop, Sanya, Jan 22-26, 2018

Global well-posedness of the anisotropic primitive equations, 26th Annual Meeting on Differential Equations and Related Topics, NTU, Jan 6-7, 2018

Global well-posedness of the anisotropic primitive equations, Recent Advances in Incompressible Flows, Capital Normal University, Dec 8-10, 2017     

10 Global well-posedness of some geophysical models: the dry dynamics Global well-posedness of some geophysical models: the moisture dynamics”, 2017 Fall Program on Analysis of PDE (Week 12), Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China, Nov.27 - Dec.1, 2017

11 “Entropy-bounded solutions of the compressible Navier-Stokes equations with far field vacuum”, Sep 25--29, 2017, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China

12 “Global strong solutions of the primitive equations without artificial vertical viscosity”, Aug 1--3, 2017, Northwest University, Xi’an China

13 Global well-posedness and relaxation limit of a tropical atmosphere model”, June 2, 2017, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan

14 Global well-posedness of the 3D anisotropic primitive equationsJune 1, 2017, Central China Norma University, Wuhan  

15 Primitive equations with horizontal viscosity and diffusivity: around $H^1$ initial data”, May 16, 2017, Technische Universitat Darmstadt, Darmstadt, Germany

16 “Global well-posedness of anisotropic primitive equations”, May 9, 2017, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany

17 “Global well-posedness of the primitive equations of oceanic and atmospheric dynamics”, February 16, 2017, ICERM, Brown University, Providence, USA

18 Global well-posedness of the primitive equations: near $H^1$ initial data”, December 30, 2016, IMS, The Chinese University of Hong Kong, Hong Kong

19 Recent advances on the primitive equations of oceanic and atmospheric dynamics (I)(II)”, December 13, 2016, Xiamen University, Xiamen, China

20 Global well-posedness of the primitive equations: with horizontal viscosity and vertical diffusivity (I)(II)(III)”, December 1,8,12, 2016, IMS, The Chinese University of Hong Kong, Hong Kong

21 Global well-posedness of the primitive equations: near $H^1$ initial data (I)(II)”, November 18,22, 2016, IMS, The Chinese University of Hong Kong, Hong Kong

22 Recent advances on the primitive equations of oceanic and atmospheric dynamics, October 31, 2016, IMS, The Chinese University of Hong Kong, Hong Kong

23 Recent advances on the primitive equations of oceanic and atmospheric dynamics”, September 17, 2016, South China Normal University, Guangzhou, China  

24 Recent advances on the primitive equations of oceanic and atmospheric dynamics”, May 19, 2016, Vanderbilt University, Nashville

25 “Global well-posedness and relaxation limit for a tropical atmosphere model (I) (II)”, Jan 29, 2016, IMS CUHK, Hong Kong

26 Recent advances on the primitive equations of oceanic and atmospheric dynamics, Dec 17, 2015, Wolfgang Pauli Institute (WPI) , Vienna

27 Global well-posedness of strong solutions to the 3D primitive equations with partial dissipation, Nov 30, 2015, Fudan University, Shanghai

28 A tropical atmosphere model: global well-posedness and relaxation limit, Aug 14, 2015, Oberwolfach, Germany

29 Global well-posedness of strong solutions to the 3D anisotropic primitive equations for large-scale oceanic and atmospheric flow with horizontal viscosity and vertical diffusivity, Jul 7, 2015, IMS, The Chinese University of Hong Kong

30 “Global existence of strong solutions to the 3D primitive equations for large-scale atmospheric and oceanic flow with partial dissipation”, Jul 13, 2015, Dalian, China

31 "The primitive equations with partial dissipation", May 14, 2015, Naharlya, Israel

32 “The primitive equations with partial dissipation”, March 1, 2015, Oklahoma State University

33 “Some results on the three-dimensional primitive equations”, February 3, 2015, Texas A&M University

34 “The primitive equations with partial dissipation”, Jan 8, 2015, Texas A&M University

35 "Some recent developments on the primitive equations with partial dissipation", Dec 30, 2014, Technion

36 “Primitive equations with only horizontal dissipation”, Nov 25, 2014, Jiangxi Normal University

37 “Some mathematical studies on the primitive equations”, Nov 24, 2014, Yichun University

38  “Local well-posedness of strong solutions to the Ericksen-Leslie system”, Oct 17, 2014, IMS, The Chinese University of Hong Kong

39 “Global strong solutions to the 3D primitive equations with only horizontal viscosities and diffusivity”, Fourth Workshop on Fluid and PDE, May 26 -- 30, 2014, IMPA, Rio de Janeiro, Brazil

40 “Convergence from Ginzburg-Landau system to Ericksen-Leslie system”, April 30, 2014, IMPA, Rio de Janeiro, Brazil

41 “Primitive equations modeling atmospheric and oceanic dynamics”, March 19, 2014, Faculty retreat (Faculty of Mathematics and Computer Science, Weizmann Institute of Science)

42 “Global strong solutions to the 3D primitive equations with only horizontal dissipation”, Jan 21, 2014, IMS, The Chinese University of Hong Kong


SHORT TIME VISITS

1. Department of Mathematics, Texas A&M, March 16 -- May 15, 2016

2. Wolfgang Pauli Institute (WPI) , Dec 13--22, 2015

3. Department of Mathematics, Texas A&M, January 6 -- March 5, 2015

4. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, October 13 – 19, 2014

5. Instituto Nacional de Mathematica Purae Applicada (IMPA) April 7 – June 6, 2014

6. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, January 16 – 23, 2014


TEACHING EXPERIENCE

1. MATH3270B Ordinary Differential Equations: Summer 2018

2. MATH 3270A Ordinary Differential Equations: Fall 2016


PUBLISHED RESEARCHPAPERS

1.  With Tao Huang and Huajun Gong, Nonuniqueness of nematic liquid crystal flows in dimension three, J. Differential Equations 263 (2017), no. 12, 8630–8648.

2.  With Sabine Hittmeir, Rupert Klein, and Edriss S Titi: Global well-posedness for passively transported nonlinear moisture dynamics with phase changes, Nonlinearity 30 (2017) 3676–3718

3.  Local existence and uniqueness of strong solutions to the Navier–Stokes equations with nonnegative density. J. Differential Equations 263 (2017), no. 10, 6512–6536. 

4.  With Chongsheng Cao and Edriss S. Titi: Strong solutions to the 3D primitive equations with only horizontal dissipation: Near $H^1$ initial data, J. Funct. Anal. 272 (2017), no. 11, 4606–4641.

5.  With Edriss S. Titi: Existence and uniqueness of weak solutions to viscous primitive equations for certain class of discontinuous initial data, SIAM J. Math. Anal. 49 (2017), no. 1, 1–28.

6.  With Huajun Gong and Chen Xu: Local well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie stress tensor, Z. Angew. Math. Phys. 68 (2017), no. 1, 68:17.

7.  With Huajun Gong and Chen Xu: Local well-posedness of strong solutions to density-dependent liquid crystal system, Nonlinear Anal. 147 (2016), 26–44.

8.  With Edriss S. Titi: Recent advance concerning certain class of geophysical flows. (``Handbook of Mathematical Analysis in Viscous Fluid”)

9. With Zhouping Xin: Global weak solutions to non-isothermal nematic liquid crystals in 2D. Acta Math. Sci. Ser. B Engl. Ed. 36 (2016), no. 4, 973–1014.

10. With Edriss S. Titi: A tropical atmosphere model: global well-posedness and relaxation limit. Nonlinearity, 29 (2016) 2674–2714.

11. With Chongsheng Cao and Edriss S. Titi: Global well-posedness of the 3D primitive equations with only horizontal viscosity and diffusion. Comm. Pure Appl. Math., 69 (2016), 1492--1531.

12. With Edriss S. Titi and Zhouping Xin: On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in $R^2$. Math. Models Methods Appl. Sci. 26 (2016), 803--822.

13. With Edriss S. Titi: Global well-posedness of strong solutions to the tropical climate model. (invited paper submitted to DCDS on the occasion of the 90th birthday of Professor Peter Lax), Discrete Contin. Dyn. Syst. 36 (2016), 4495--4516. 

14. With Edriss S. Titi: Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Arch. Rational Mech. Anal. 220 (2016), 983--1001. 

15. With Jishan Fan: A logarithmic regularity criterion for the 3D generalized MHD system. Math. Methods Appl. Sci. 38 (2015), 5279--5283. 

16. With Jishan Fan: Regularity criteria for the strong solutions to the Ericksen-Leslie system in $R^3$. J. Math. Anal. Appl. 425 (2015), no. 2, 695–703.

17. Global strong solutions to Incompressible nematic liquid crystal flow. Methods and Applications of Analysis, 22 (2015), no.2, 201--220.

18. With Chongsheng Cao and Edriss S. Titi:Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. J. Differential Equations 257 (2014), no. 11, 4108–4132.

19. With Chongsheng Cao and Edriss S. Titi:Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity. Arch. Ration. Mech. Anal. 214 (2014), no. 1, 35–76.

20. With Wenya Ma and Huajun Gong, Global strong solutions to incompressible Ericksen–Leslie system in $R^3$. Nonlinear Anal.  109 (2014), 230–235.

21. With Minchun Hong and Zhouping Xin: Blow up criteria of strong solutions to the Ericksen-Leslie system in R^3. Comm. Partial Differential Equations, 39, 2014, 1284 - 1328

22. Global strong and weak solutions to inhomogeneous nematic liquid crystal flow in two dimensions.Nonlinear Anal. 99 (2014), 80–94.

23. With Huajun Gong: Global existence of strong solutions to incompressible MHD. Commun. Pure Appl. Anal.13 (2014), no. 3, 1337–1345.

24. With Jin-Xue Yin and Yuan-Yuan Ke: Existence of positive solutions for the p(x)-Laplacian equation., Rocky Mountain J. Math. 42 (2012), no. 5, 1675–1758.

25. With Jin-Xue Yin and Yuan-Yuan Ke: Existence of positive solutions for the p-Laplacian with p-gradient term.J. Math. Anal.Appl. 383 (2011), 

no. 1,  147–158.

26. With Jin-Xue Yin and Yuan-Yuan Ke: Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection., Appl. Anal. 89 (2010), no. 10, 1575–1590.


SUBMITTED RESEARCHPAPERS AND PREPRINTS

1. Global well-posedness of the 1D compressible Navier-Stokes equations with constant heat conductivity and nonnegative density,  arXiv:1801.09395

2. With Zhouping Xin, Entropy-bounded solutions of the compressible Navier-Stokes equations with far field vacuum, arXiv:1710.06571

3. With Chongsheng Cao and Edriss S. Titi: Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity, arXiv:1703.02512 

4. With Meng Wang, Wendong Wang and Zhouping Xin: Unified blow-up  criteria for abstract dynamical systems and the applications to liquid crystals (preprint)

5. With Zhouping Xin: Finite time blow up of compressible Navier-Stokes

  equations on half space or outside a fixed ball. (complete)

6. With Edriss S. Titi: The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: regorous justification of the hydrostatic approximation. arXiv:1706.08885

7. Liquid Crystal equations with infinite energy: local well-posedness and blow up criteria.  arXiv:1309.0072


Journals Refereed

Nonlinarity; Journal of Mathematical Physics; Applicable Analysis; Journal of Nonlinear Science; Journal dAnalyse Mathematique; Mathematical Methods in the Applied Sciences; DCDS-A; Nonlinear Analysis; JMAA; Zeitschrift fur angewandte Mathematik und Physik ZAMP