Geng Chen
I am an Associate Professor in Department of mathematics, at University of Kansas.
Office: 623 Snow Hall
Email: gengchen at ku dot edu
Here is my
CV (updated on Feb 2020)
Teaching in Fall 2020
Math 220. Find class information on Blackboard.
Research interests
I have a broad interest on analysis, partial differential equations, fluid dyanmics, mathematical physics. My current research focuses on the wellposedness and behaviors of solutions for the following equations.
Two slides for my research: Euler equations , Nonlinear wave equations and water waves.
Publications
My research is partially supported by NSF grants:
DMS1715012, 20172021;
DMS2008504, 20202023.

Uniqueness and weakBV stability for 2x2 conservation laws, submitted, (with Sam G. Krupa and Alexis F. Vasseur) available at
ArXiv

Uniqueness of Dissipative Solution for CamassaHolm Equation with PeakonAntipeakon Initial Data, to appear in Applied Mathematics Letters, (with Hong Cai and Hongwei Mei) available at
ArXiv

A Finsler type Lipschitz optimal transport metric for a quasilinear wave equation, submitted, (with Hong Cai and Yannan Shen) available at
ArXiv

Uniqueness of conservative solutions to a onedimensional general quasilinear wave equation through variational principle, submitted, (with Hong Cai, Yi Du and Yannan Shen), available at
ArXiv

Vanishing Viscosity Limit of the ThreeDimensional Barotropic Compressible NavierStokes Equations with Degenerate Viscosities and FarField Vacuum, to appear in Annales de l'Institut Henri Poincare, Analyse non lineaire., (with GuiQiang Chen and Shengguo Zhu) available at
ArXiv

Singularity formation for radially symmetric expanding wave of Compressible Euler Equations, submitted,
(with Hong Cai, TianYi Wang) available at
ArXiv

Poiseuille flow of nematic liquid crystals via the full EricksenLeslie model, submitted,
(with Tao Huang, Weishi Liu) Arch. Ration. Mech. Anal., 236 (2020), 839891.
ArXiv

Formation of Singularities and Existence of Global Continuous Solutions for the Compressible Euler Equations, submitted, (with GuiQiang G. Chen, Shengguo Zhu)
ArXiv

Optimal density lower bound on nonisentropic gas dynamics, J. Differential Equations, 268 (2020), no. 7, 40174028.
ArXiv

On finite time BV blowup for the psystem,
Communications in Partial Differential Equations 43 (2018), no. 8, 1242–1280. (with Alberto Bressan and Qingtian Zhang).
pdf

A polygonal scheme and the lower bound on density for the isentropic gas dynamics, DCDS 39 (2019), no. 7, 42594277. (with Ronghua Pan and Shengguo Zhu).
pdf

The almost global existence for a 3D wave equation of nematic liquidcrystals, (with Yi Du and Jianli Liu). Contemporary Mathematics, volum 725, 2019.
ArXiv

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

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

Generic regularity and Lipschitz metric for the HunterSaxton type equations,
J. Differential Equations 262, 10231063 (2017) (with Hong Cai, Yannan Shen and Zhong Tan).
pdf

Lipschitz metric for conservative solutions of the twocomponent CamassaHolm system,
Z. Angew. Math. Phys. (ZAMP) 68 (2017), no. 1, 516 (with Hong Cai and Yannan Shen).
pdf

Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation, Indiana Univ. Math. J. 67 (2018), 23932433 (with Ming Chen and Yue liu).
ArXiv
 Optimal timedependent lower bound on density for classical solutions of 1D
compressible Euler equations, Indiana Univ. Math. J., 66 (2017), No. 3, 725–740. pdf
 Lipschitz metric for a class of nonlinear wave equations, Arch. Ration. Mech. Anal. 226 (2017) no. 3, 1303–1343 (with Alberto Bressan). pdf

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

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

Unique conservative solutions to a variational wave equation, Arch. Ration. Mech. Anal. 217, (2015), no. 3, 10691101. (with Alberto Bressan, Qingtian Zhang). pdf

Existence and regularity of solutions in nonlinear wave equations,
Discrete Contin. Dyn. Syst., Series A,
35 (2015), no. 8, 33273342. (with Yannan Shen).
pdf

No BV bounds for approximate solutions to psystem with general pressure law,
J. Hyper. Differential Equations, 12(2015), 799816.(with Alberto Bressan, Qingtian Zhang and Shengguo Zhu). pdf

Finite time singularities for hyperbolic systems, SIAM J. Math. Anal.
47 (2015), no. 1, 758785, (with Tao Huang and Chun Liu).
pdf

Shock formation and exact solutions
for the compressible Euler equations, Arch. Ration. Mech. Anal., 217 (2015), no. 3, 12651293. (with Robin Young). ArXiv

Uniqueness of Conservative Solutions to the
CamassaHolm Equation via Characteristics, Discrete Contin. Dyn. Syst., Series A,
35 (2015), no. 1, 2542.
(with Alberto Bressan and Qingtian Zhang). pdf

Lack of BV Bounds for Approximate Solutions to
the psystem with Large Data, J. Differential Equations 256 (2014), 30673085 (with Alberto Bressan and Qingtian Zhang). pdf

No TVD fields for 1d isentropic gas flow, Comm. Partial Differential Equations, 38 (2013), no. 4, 629657 (with Helge Kristian Jenssen). ArXiv

Existence and singularity to a wave system of nematic liquid crystals, J. Math. Anal. Appl., 398 (2013), 170188 (with Yuxi Zheng).

Shock formation in the compressible Euler equations and related systems, J. Hyper. Differential Equations, 10 (2013), no. 1, 149172 (with Robin Young and Qingtian Zhang). pdf

Conservation solutions to a system of variational wave equations of nematic liquid crystals, Comm. Pure Appl. Anal., 12 (2013), no. 3, 14451468 (with Ping Zhang and Yuxi Zheng). pdf

Pairwise wave interactions in ideal polytropic gases, Arch. Ration. Mech. Anal., 204 (2012), no. 3, 787836, (with Erik Endres and Helge Kristian Jenssen).

Vacuum in the nonisentropic gas dynamics, Acta Mathematica Scientia, 32 (2012), 339351, no. 1, (with Robin Young). (Special issue for Constantine M. Dafermos' 70th birthday.)

Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation, J. Differential Equations, 252 (2012), no. 3, 25802595, (with Robin Young).
 Formation of singularity and smooth wave propagation for the nonisentropic compressible Euler equations, J. Hyper. Differential Equations, 8 (2011), no. 4, 671690.

Disease persistence for a kind of agestructured epidemic models (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 22 (2007), no. 3, 253262.

SARS epidemic model and its application (in Chinese), Appl. Math. J. Chinese Univ. Ser. A, 21 (2006), no. 3, 253263, (with Yuanjun Wang).
Workshop
Workshop on Nonlinear Differential Equations, Dynamical Systems and Applications, Oct 2021, 2018, University of Kansas, organized by Geng Chen and Weishi Liu. For the link of the workshop, click here.