Global large strong solutions to the radially symmetric compressible Navier-Stokes equations in 2D solid balls

Abstract

In this paper, we consider the initial-boundary value problems of the compressible isentropic Navier-Stokes equations with density-dependent viscosity on two dimensional solid balls which was first introduced by Kazhikhov where shear viscosity $\mu$ is assumed to be constant and the bulk viscosity $\lambda$ is a polynomial of density up to power $\beta$. Under the condition of $\beta>1$, we prove the global existence of the radially symmetric strong solutions to the Kazhikhov models under Dirichlet boundary conditions for arbitrary large initial smooth data. Moreover, the density is shown to be uniformly bounded with respect to time when $\beta\in (\max\{1,\frac{\gamma+2}{4}\},\gamma]$. This improves the previous result of \cite{2016Huang,2022Huang} for general 2D domains where they require $\beta>4/3$ to ensure global existence and is the first result concerning the global existence of classical solutions to the radially symmetric compressible Navier-Stokes equations in 2D solid balls under Dirichlet boundary condition.