Existence and Blowup Behavior of Global Strong Solutions to the Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data

Xiangdi Huang, Jing Li

Published 2012-05-24, updated 2012-06-16Version 2

For periodic initial data with initial density allowed to vanish, we establish the global existence of strong and weak solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data provided the bulk viscosity coefficient is $\lambda = \rho^{\beta}$ with $\beta>4/3$. These results generalize and improve the previous ones due to Vaigant-Kazhikhov([Sib. Math. J. (1995), 36(6), 1283-1316]) which requires $\beta>3$. Moreover, both the uniform upper bound of the density and the large-time behavior of the strong and weak solutions are also obtained.