Geng Chen

I am an Associate Professor in Department of mathematics, at University of Kansas.

Office: 522 Snow Hall

Email: gengchen at ku dot edu

Here is my CV (updated on Sep 2022)

Teaching

Research interests

I have a broad interest on analysis, partial differential equations, fluid dyanmics, mathematical physics. My current research focuses on the well-posedness and behaviors of solutions for the following equations.

• Compressible Euler equations, conservation laws, Navier-Stokes equations.
• Nonlinear wave equations with applications on liquid crystal and elasticity, optimal transport metric.
• Models for shallow water waves, Camassa-Holm equation.

Two slides for my research: Euler equations , Nonlinear wave equations and water waves.

Publications

My research is partially supported by NSF grants: DMS-2306258, 2023-2026; DMS-2008504, 2020-2024. DMS-1715012, 2017-2021;

1. From Navier-Stokes to BV solutions of the barotropic Euler equations (with Moon-Jin Kang and Alexis F. Vasseur), available at ArXiv.

2. BV solutions to a hyperbolic system of balance laws with logistic growth, (with Yanni Zeng) submitted, available at ArXiv.

3. Generic Singularities for 2D Pressureless Flow, (with Albeto Bressan and Shoujun Huang) submitted, available at ArXiv

4. Initial-boundary value problems for Poiseuille flow of nematic liquid crystal via full Ericksen-Leslie model, (with Yanbo Hu and Qingtian Zhang) submitted, available at ArXiv

5. The Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals: The general Case, to appear in JDE (with Weishi Liu and Majed Sofiani), available at ArXiv

6. Lipschitz optimal transport metric for a wave system modeling nematic liquid crystals, submitted (with Hong Cai and Yannan Shen) available at ArXiv

7. Singularity formation for full Ericksen-Leslie system of nematic liquid crystal flows in dimension two, submitted (with Tao Huang and Xiang Xu) available at ArXiv

8. Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to lambda-family equations, to appear in Quarterly of Applied Mathematics. (with Shihui Zhu and Yannan Shen) available at ArXiv

9. Singularity formation for the general Poiseuille flow of nematic liquid crystals, Communications on Applied Mathematics and Computation (by invitation) 5 (2023), no. 3, 1130–1147. (with Majed Sofiani) available at ArXiv

10. Uniqueness and weak-BV stability for 2x2 conservation laws, Arch. Ration. Mech. Anal. 246 (2022), no. 1, 299–332. (with Sam G. Krupa and Alexis F. Vasseur) available at ArXiv

11. Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data, Applied Mathematics Letters 120 (2021), Paper No. 107268, 8. (with Hong Cai and Hongwei Mei) available at ArXiv

12. A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation, J. Differential Equations, 356 (2023), 289–335. (with Hong Cai and Yannan Shen) available at ArXiv

13. Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle, J. Math. Phys. 63 (2022), no. 2, Paper No. 021508, 21., (with Hong Cai, Yi Du and Yannan Shen), available at ArXiv

14. Vanishing Viscosity Limit of the Three-Dimensional Barotropic Compressible Navier-Stokes Equations with Degenerate Viscosities and Far-Field Vacuum, Annales de l'Institut Henri Poincare, Analyse non lineaire., 39 (2022), no 1, 121–170. (with Gui-Qiang Chen and Shengguo Zhu) available at ArXiv

15. Singularity formation for radially symmetric expanding wave of Compressible Euler Equations, to appear in SIAM J. Math. Anal., (with Hong Cai, Tian-Yi Wang) available at ArXiv

16. Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model, submitted, (with Tao Huang, Weishi Liu) Arch. Ration. Mech. Anal., 236 (2020), 839-891. ArXiv

17. Formation of Singularities and Existence of Global Continuous Solutions for the Compressible Euler Equations, SIAM J. Math. Anal. 53 (2021), no. 6, 6280–6325 (with Gui-Qiang G. Chen, Shengguo Zhu) ArXiv

18. Optimal density lower bound on nonisentropic gas dynamics, J. Differential Equations, 268 (2020), no. 7, 4017-4028. ArXiv

19. On finite time BV blow-up for the p-system, Communications in Partial Differential Equations 43 (2018), no. 8, 1242–1280. (with Alberto Bressan and Qingtian Zhang). pdf

20. A polygonal scheme and the lower bound on density for the isentropic gas dynamics, DCDS 39 (2019), no. 7, 4259-4277. (with Ronghua Pan and Shengguo Zhu). pdf
21. The almost global existence for a 3-D wave equation of nematic liquid-crystals, (with Yi Du and Jianli Liu). Contemporary Mathematics, volum 725, 2019. ArXiv

22. Uniqueness and regularity of conservative solution to a wave system modeling nematic liquid crystal, J. Math. Pures Appl. (9) 117 (2018), 185–220. (with Hong Cai, Yi Du). pdf

23. Lipschitz metric for the Novikov equation, Arch. Ration. Mech. Anal. 229 (2018), no. 3, 1091–1137 (with Hong Cai, Robin Ming Chen and Yannan Shen). pdf

24. Generic regularity and Lipschitz metric for the Hunter-Saxton type equations, J. Differential Equations 262, 1023-1063 (2017) (with Hong Cai, Yannan Shen and Zhong Tan). pdf

25. Lipschitz metric for conservative solutions of the two-component Camassa-Holm system, Z. Angew. Math. Phys. (ZAMP) 68 (2017), no. 1, 5-16 (with Hong Cai and Yannan Shen). pdf

26. Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation, Indiana Univ. Math. J. 67 (2018), 2393-2433 (with Ming Chen and Yue liu). ArXiv

27. Optimal time-dependent lower bound on density for classical solutions of 1-D compressible Euler equations, Indiana Univ. Math. J., 66 (2017), No. 3, 725–740. pdf

28. Lipschitz metric for a class of nonlinear wave equations, Arch. Ration. Mech. Anal. 226 (2017) no. 3, 1303–1343 (with Alberto Bressan). pdf

29. Generic structure of conservative solutions to a nonlinear wave equation, Annales de l'Institut Henri Poincare, Analyse non lineaire., 34 (2017), no. 2, 335–354 (with Alberto Bressan). pdf

30. Singularity formation for compressible Euler equations, SIAM J. Math. Anal., 49 (2017), no. 4, 2591–2614. (with Ronghua Pan and Shengguo Zhu). pdf

31. Unique conservative solutions to a variational wave equation, Arch. Ration. Mech. Anal. 217, (2015), no. 3, 1069-1101. (with Alberto Bressan, Qingtian Zhang). pdf

32. Existence and regularity of solutions in nonlinear wave equations, Discrete Contin. Dyn. Syst., Series A, 35 (2015), no. 8, 3327-3342. (with Yannan Shen). pdf
33. No BV bounds for approximate solutions to p-system with general pressure law, J. Hyper. Differential Equations, 12(2015), 799-816.(with Alberto Bressan, Qingtian Zhang and Shengguo Zhu). pdf

34. Finite time singularities for hyperbolic systems, SIAM J. Math. Anal. 47 (2015), no. 1, 758-785, (with Tao Huang and Chun Liu). pdf
35. Shock formation and exact solutions for the compressible Euler equations, Arch. Ration. Mech. Anal., 217 (2015), no. 3, 1265-1293. (with Robin Young). ArXiv
36. Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics, Discrete Contin. Dyn. Syst., Series A, 35 (2015), no. 1, 25-42. (with Alberto Bressan and Qingtian Zhang). pdf
37. Lack of BV Bounds for Approximate Solutions to the p-system with Large Data, J. Differential Equations 256 (2014), 3067-3085 (with Alberto Bressan and Qingtian Zhang). pdf

38. No TVD fields for 1-d isentropic gas flow, Comm. Partial Differential Equations, 38 (2013), no. 4, 629-657 (with Helge Kristian Jenssen). ArXiv
39. Existence and singularity to a wave system of nematic liquid crystals, J. Math. Anal. Appl., 398 (2013), 170-188 (with Yuxi Zheng).
40. Shock formation in the compressible Euler equations and related systems, J. Hyper. Differential Equations, 10 (2013), no. 1, 149-172 (with Robin Young and Qingtian Zhang). pdf
41. Conservation solutions to a system of variational wave equations of nematic liquid crystals, Comm. Pure Appl. Anal., 12 (2013), no. 3, 1445-1468 (with Ping Zhang and Yuxi Zheng). pdf
42. Pairwise wave interactions in ideal polytropic gases, Arch. Ration. Mech. Anal., 204 (2012), no. 3, 787-836, (with Erik Endres and Helge Kristian Jenssen).
43. Vacuum in the non-isentropic gas dynamics, Acta Mathematica Scientia, 32 (2012), 339-351, no. 1, (with Robin Young). (Special issue for Constantine M. Dafermos' 70th birthday.)
44. Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation, J. Differential Equations, 252 (2012), no. 3, 2580-2595, (with Robin Young).
45. Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations, J. Hyper. Differential Equations, 8 (2011), no. 4, 671-690.
46. Disease persistence for a kind of age-structured epidemic models (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 22 (2007), no. 3, 253-262.
47. SARS epidemic model and its application (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 21 (2006), no. 3, 253-263, (with Yuanjun Wang).

Workshop

Workshop on Nonlinear Differential Equations, Dynamical Systems and Applications, Oct 20-21, 2018, University of Kansas, organized by Geng Chen and Weishi Liu. For the link of the workshop, click here.