具超音速边界可压Navier-Stokes方程解的指数衰减

Exponential Decay of Solutions to the Compressible Navier-Stokes Equations with a Supersonic Boundary

考虑了二维空间上具超音速物理边界的可压Navier—Stokes方程的初边值问题．给定常数平衡态（P＊，0），得到了所考虑问题解的整体存在性．在平衡态附近的小扰动下，利用加权能量估计方法得到解的指数衰减性．

This paper considers an initial-boundary value problem of compressible Navier- Stokes equations with a supersonic physical boundary in two dimensions. Given a constant equilibrium state （p＊, 0）, the authors construct the global existence of solutions. By using weighted energy estimates, it is shown that the solution converges to the equilibrium state with an exponential rate when the perturbations are sutticiently small.