Global behavior of 1D compressible isentropic Navier-Stokes equations with a non-autonomous external force
College of Mathematics and Information Science, North China University of Water Sources and Electric Power, Zhengzhou 450011, People's Republic of PR China
Boundary Value Problems 2011, 2011:43 doi:10.1186/1687-2770-2011-43Published: 3 November 2011
In this paper, we study a free boundary problem for compressible Navier-Stokes equations with density-dependent viscosity and a non-autonomous external force. The viscosity coefficient μ is proportional to ρθ with 0 < θ < 1, where ρ is the density. Under certain assumptions imposed on the initial data and external force f, we obtain the global existence and regularity. Some ideas and more delicate estimates are introduced to prove these results.