The evolution compressible Navier-Stokes system on polygonal domains

Abstract

The evolution compressible Navier-Stokes system is considered on polygonal domains. It is shown that the lowest order of the corner singularity of the system is the same as that of the heat equation. In a suitable Banach space the velocity is split into singular and regular parts and the coefficient of the singularity is expressed by convolution of some two functions in the time variable. By a formula of the pressure we observe propagation of the corner singularity along the characteristic lines emanating from the corners and also unboundedness of derivatives of pressure there. An increased regularity for the remainder part is established. (c) 2006 Elsevier Inc. All rights reserved.