Decay Rates For The Strong Solutions To The Compressible Navier-Stokes Equations Without Heat Conductivity

In this paper,we consider the compressible Navier-Stokes equations without heat conductivity in R~3.The global existence and uniqueness of strong solutions are established when the initial value towards its equilibrium is sufficiently small in~2(R~3).By using the low frequency and high frequency decomposition,the key uniform bound of entropy is obtained,even though the entropy is non-dissipative due to the absence of heat conductivity.Moreover,the time decay rates of global solutions are also obtained without the~1boundedness of initial perturbations.This result extends the following works:Duan-Ma(2008),Tan-Wang(2016)and Tan-Wang(2012).This paper can be divided into the following four parts:In Chapter 1,we introduce some related backgrounds about the compress-ible viscous fluids model,the trend of the relevant scholars about this model and the related model at home and abroad and the method of this paper.In Chapter 2,the main conclusions of this paper are given and reformulate the model.In Chapter 3,we obtained the energy estimates about the low frequency component and high frequency component of the solutions by using the low frequency and high frequency decomposition.In Chapter 4,we proved the global existence,uniqueness and obtained the decay rates of solutions of the cauchy problem to the compressible Navier-Stokes equations without heat conductivity by combining a series of the priori estimates of the solution.