From the 1 of 8 linked papers with an AI index.
8 papers
The contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
Geng Chen, Harish Ravichandar, Yannan Shen
The paper proves that planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev‑Petviashvili equation and the multi‑dimensional KdV‑Burgers equation con…
Complex Dynamics of Wave-Character Transitions in Radially Symmetric Isentropic Euler Flows: Theory and Numerics
Eduardo Abreu, Geng Chen, Faris El-Katri +1
We investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive…
-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…
Existence and singularity formation for the supersonic expanding wave of radially symmetric non-isentropic compressible Euler equations
Geng Chen, Faris A. El-Katri, Yanbo Hu
This paper studies the existence and singularity formation of supersonic expanding waves for the radially symmetric non-isentropic compressible Euler equations of polytropic gases.…
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…
Quantitative weak-BV stability of "wild'' solutions to compressible Euler equations, with a view towards higher systems
Geng Chen, Cooper Faile, Sam G. Krupa
For hyperbolic systems of conservation laws, including important physical models from continuum mechanics, the question of stability for large data solutions remains a challenging…