Global Regularity to the Two Dimensional Compressible Navier-Stokes Equations with Mass Diffusion
For an isentropic compressible Navier-Stokes model with mass diffusion in a two dimensional bounded smooth domain, global existence and uniqueness of strong solution to the initial-boundary value problem is proved, without any size restriction on the initial data. The proof relies on global upper and lower positive bound for the density, which is a consequence of mass diffusion and obtained by De Giorgi-Nash-Mosers estimate for solution to the second order parabolic equation.
global regularity initial-boundary value problem brenners navier-stokes equations 35q30 35a05