44 citations · 176 across the 20 of their papers we have counts for
11 papers · 1 filter
Structurally stable singularities and Lipschitz stable optimal transport metrics for the compressible Euler equations
Geng Chen, Yanbo Hu, Yannan Shen
It is well known that solutions to the compressible Euler equations can develop singularities in finite time. In this paper, we carry out a detailed analysis on behaviors of soluti…
The contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
Geng Chen, Harish Ravichandar, Yannan Shen
In this paper, we show the contraction property of the planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev-Petviashvili (KP) equation modell…
-contraction of Shock Waves for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave sol…
Uniform Stability of Oscillatory Shocks for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, inclu…
Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the inva…
Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new defin…
Lipschitz optimal transport metric for a wave system modeling nematic liquid crystals
Hong Cai, Geng Chen, Yannan Shen
In this paper, we study the Lipschitz continuous dependence of conservative Hölder continuous weak solutions to a variational wave system derived from a model for nematic liquid cr…
Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to -family equations
Geng Chen, Yannan Shen, Shihui Zhu
In this paper, we prove the global existence of Hölder continuous solutions for the Cauchy problem of a family of partial differential equations, named as -family equations, whe…
Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle
Hong Cai, Geng Chen, Yi Du +1
In this paper, we prove the uniqueness of energy conservative Holder continuous weak solution to a general quasilinear wave equation by the analysis of characteristics. This result…
Lipschitz metric for the Novikov equation
Hong Cai, Geng Chen, Robin MIng Chen +1
We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport…
Existence and regularity of solutions in nonlinear wave equations
Geng Chen, Yannan Shen
In this paper, we study the global existence and regularity of Hölder continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.