Green's Function of 2-D Compressible Navier- Stokes Equations on the Half Space

Abstract

Solutions of 2-D compressible Navier-Stokes equations are discussed here, especially solutions of whose linearized form around a constant state with presence of zero Dirichlet boudary. It is devided into three parts. Firstly, Green's identity of linearized 2-D compressible Navier-Stokes are studied. Secondly, Master Relation and wave propagators are introduced, and structures of these wave propagators are shown. Master Relation reveals essential connections between boundary data, which is key factors to construct below Green's function. It can also be observed that Master Relation is composition of two types of wave propagators: one called the interior wave propagator and the other surface the wave propagator. At last, Green's function of linearized 2-D compressible Navier-Stokes equations with presence of zero Dirichlet boundary data is represented. With integration of the fundamental solution and Master Relation, Green's function can be represented explicitly. Structures of wave propagators help us to achieve its whole picture.