Incompressible Limit And Stability Of Two Kinds Of Hydrodynamic Equations

The study of mathematical theory of hydrodynamics aims to explore the motion and laws of fluids(such as gas,liquid,etc.),which involves some basic mathematical models,among which the Navier-Stokes equations and Oldroyd-B model are very important models in physics and mathematics.This paper presents a study on the local existence and uniqueness of strong solutions for the Oldroyd-B model of incompressible viscoelastic fluids in a bounded domain with density-dependent viscosity,as well as the exponential asymptotic stability of global solutions of the three-dimensional non-isentropic compressible Navier-Stokes equations.The main findings are presented below:Firstly,the compressible Oldroyd-B model with the initial condition of "wellprepared" and velocity satisfying the slip boundary condition is considered in the case of density-dependent viscosity,and the incompressible limit of local strong solutions of the model is obtained.Based on the conclusion of the incompressible limit,this paper will further deduce and prove the existence and uniqueness of local strong solutions for the Oldroyd-B model,which is the extension of the constant viscosity coefficient case.The main idea is to derive a uniform energy estimate for the linearized system with respect to the Mach number,which leads to a uniform energy estimate for the nonlinear system and the corresponding incompressible limit.Secondly,the three-dimensional non-isentropic Navier-Stokes equations with the initial condition of "well-prepared" and the velocity and temperature satisfy the Dirichlet boundary conditions and convective boundary conditions respectively are considered,and the exponential asymptotic stability of the equations is studied.The main idea is to obtain the exponential asymptotic stability of the global solution for the compressible NavierStokes equations and its incompressible limit according to the incompressible limit conclusion and the repeated derivation of the uniform energy estimate.Figure [0] Table [0] Reference [78]...