Free boundary value problem for the radial symmetric compressible isentropic Navier-Stokes equations with density-dependent viscosity

This paper is devoted to the study of free-boundary-value problem of the compressible Naiver-Stokes system with density-dependent viscosities mu = const > 0, lambda = rho(beta) which was first introduced by Vaigant-Kazhikhov [23] in 1995. By assuming the endpoint case beta = 1 in the radially spherical symmetric setting, we prove the (a priori) expanding rate of the free boundary is algebraic for multidimensional flow, and particularly establish the global existence of strong solution of the two-dimensional system for any large initial data. This also improves the previous work of Li-Zhang [14] where they proved the similar result for beta > 1. The main ingredients of this article is making full use of the geometric advantage of domain as well as the critical space dimension two. (c) 2025 Published by Elsevier Inc.