242 citations · 250 across the 7 of their papers we have counts for
7 papers · 1 filter
Global well-posedness of the Cauchy problem for the modified Whitham equations
Han Cui, Yuexun Wang, Zhouping Xin
This paper aims to show global existence and modified scattering for the solutions of the Cauchy problem to the modified Whitham equations for small, smooth and localized initial d…
Global-in-time Well-posedness of Classical Solutions to the Vacuum Free Boundary Problem for the 1-D Viscous Saint-Venant System with Large Data
Xin Zhouping, Zhang Jiawen, Zhu Shengguo
We establishes the global existence and uniqueness of classical solutions to the vacuum free boundary problem for the 1-D viscous Saint-Venant system with a general class of large…
Finite time blowup of strong solutions to the two dimensional MHD equations
Xiangdi Huang, Zhouping Xin, Wei Yan
Whether the smooth solution of the multi-dimensional viscous compressible fluids will blow-up in finite time has always been a chanllenging problem. In the recent work\cite{FM}, Me…
Asymptotic stability of the equilibrium for the free boundary problem of a compressible atmospheric primitive model with physical vacuum
Xin Liu, Edriss S. Titi, Zhouping Xin
This paper concerns the large time asymptotic behavior of solutions to the free boundary problem of the compressible primitive equations in atmospheric dynamics with physical vacuu…
On the vacuum free boundary problem of the viscous Saint-Venant system for shallow water in two dimensions
Hai-Liang Li, Yuexun Wang, Zhouping Xin
In this paper, we establish the local-in-time well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow water in two…
On blowup of classical solutions to the compressible Navier-Stokes equations
Xin Zhouping, Yan Wei
We study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscou…