arXiv subjects

Chengfeng Xiong

Publications and source records attributed to Chengfeng Xiong.

5 recordsLinked to original sources

arXiv2025

Global Existence and Incompressible Limit for Compressible Navier-Stokes Equations in Bounded Domains with Large Bulk Viscosity and Large Initial Data

We investigate the barotropic compressible Navier-Stokes equations with Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial data allowing vacuum, we establish the global existence and exponential decay of weak, strong, and classical solutions when the bulk viscosity coefficient is sufficiently large, without any restrictions on the size of the initial data. Furthermore, we prove that, as the bulk viscosity coefficient tends to infinity, solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations. In particular, we establish the incompressible limit of weak solutions without assuming that the initial velocity field is divergence-free.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit of the Cauchy Problem for 2D Compressible Navier-Stokes Equations with Large Bulk Viscosity and Large Initial Data

This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk viscosity coefficient, we establish the global existence and large time behavior of weak, strong, and classical solutions. It should be mentioned that this result is obtained without any restrictions on the size of the initial data. Moreover, we demonstrate that as the bulk viscosity coefficient tends to infinity, the solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations. The incompressible limit of the weak solutions holds even without requiring the initial velocity to be divergence-free.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit for Compressible Navier-Stokes Equations with Large Bulk Viscosity Coefficient and Large Initial Data

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk viscosity coefficient is sufficiently large, without any extra restrictions on initial velocity divergence. Moreover, we demonstrate that when the bulk viscosity coefficient tends to infinity, these solutions converge to solutions to the inhomogeneous incompressible Navier-Stokes equations. For the incompressible limit of weak solutions, our results hold even without requiring the initial velocity field to be divergence-free. Our results are established by introducing time-layers to avoid imposing restrictions on the initial velocity divergence, along with estimates of $L^\infty$ norm of the effective viscous flux $G$ via a time-partitioning approach based on Gagliardo-Nirenberg inequality.

math.AP↗

arXiv2025

Nonlinearly Exponential Stability for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations with Large Potential External Forces

The large time behavior for Lions-Feireisl's finite energy weak solutions to the barotropic compressible Navier-Stokes equations with large potential external forces in three-dimensional (3D) bounded domains is considered. Although the equilibrium state of density is not a constant anymore due to the non-constant external forces, by constructing a suitable Lyapunov functional and using the extra integrability of the density, after expanding the difference of the density and its steady state in a Taylor series with respect to the difference of some power function of density and that of the steady density, it is proved that any Lions-Feireisl's finite energy weak solution would decay exponentially to the equilibrium state as time tends to infinity.

math.AP↗

arXiv2020

Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains

In one-dimensional unbounded domains, we consider the equations of a planar compressible magnetohydrodynamic (MHD) flow with constant viscosity and heat conductivity. More precisely, we prove the global existence of strong solutions to the MHD equations with large initial data satisfying the same conditions as those of Kazhikhov's theory in bounded domains (Kazhikhov 1987 Boundary Value Problems for Equations of Mathematical Physics (Krasnoyarsk)). In particular, our result generalizes the Kazhikhov's theory for the initial boundary value problem in bounded domains to the unbounded case.

math.AP↗