Global Existence And Decay Estimate Of Solution To Compressible Quantum Navier-Stokes Equations With Damping

In this paper,we study the Cauchy problem of the compressible quantum NavierStokes equations with damping in R3.We prove the global existence of the strong solution of the Cauchy problem with small initial data and obtain some decay results of the solution.We first assume that the H3-norm of the initial data is sufficiently small while the higher derivative can be arbitrarily large,derives an accurate energy estimate and constructs an interactive energy functional to derive the dissipation estimate of the solution,then the local existence of the strong solution is proved by solving an approximation system,and the global existence of strong solution is obtained by combining the uniform prior estimation and the continuity argument.In addition,the decay estimate of the solution is derived for the initial data in a homogeneous Sobolev space or Besov space with negative exponent.According to the general energy method developed by the regularity interpolation method,an important estimate is obtained,which is then transformed into an explicit inequality by using the interpolation results of the negative homogeneous space,thus the decay estimate of the solution can be obtained.In addition,the usual Lp-L2 {1≤p≤2)type decayrate is obtained without assuming that the LP norm of the initial data is sufficiently small.