POINTWISE WAVE BEHAVIOR OF THE NON-ISENTROPIC NAVIER-STOKES EQUATIONS IN HALF SPACE

In this paper, we aim to study the global well-posedness and pointwise behavior of the classical solution to one-dimensional non-isentropic compressible Navier-Stokes equations in half space. Based on H-s energy method, we first establish the global existence and uniqueness. To derive the accurate pointwise estimate of the solution, Green's function for the initial boundary value problem is investigated. It is shown that Green's function can be expressed in terms of a fundamental solution to the Cauchy problem. Then applying Duhamel's principle and nonlinear analysis yields the space-time estimate of the solution under some suitable assumptions on the initial data, which exhibits the rich wave structure. As a corollary, we prove that the solution converges to the equilibrium state at an algebraic time decay rate (1+ t)(-1/2) in L-infinity norm with respect to the spatial variable.