Asymptotic Stability Of Two Types Of Incompressible Laminar Flow Models

Instability can also occur in homogeneous fluids due to the dynamic effects of ro-tation or streamline curvature.In this paper,the asymptotic stability of incompressible rotating fluids is studied.This paper focuses on the asymptotic stability of two types of incompressible laminar flow models.One class is the asymptotic stability of three dimensional incompressible Boussi-nesq equation with velocity damping term in a certain region T~2×[-1,1].In Chapter 2,it is shown that the Boussinesq approximation is accurate when the density/temperature change is very small in this physical scenario,and our main result is the asymptotic sta-bility of a particular type of perturbation for the layered solution.The global existence or finite time blowup of smooth solutions of three dimensional incompressible Navier-Stokes equations with large initial values is one of the most prominent open problems.For incompressible Boussinesq systems,there are many unsolved problems even in the two-dimensional case.This paper extends the result of[4]from two to three dimension-s.In order to obtain the asymptotic stability of stratified flow,we use energy weighting,linear decay and Duhamel's formula.The other is to study the asymptotic stability of small perturbations in three di-mensional MHD system under rotation effect.Since incompressible N-S equations and incompressible MHD equations have similar nonlinear structures,the study of MHD system is also very difficult.In this paper,we refer to[26]and[25]to study the ro-tation effect and the treatment of strong coupling structure on this basis.In order to obtain the asymptotic stability of the solution,the cylindrical coordinate change,the ellipse estimation and the continuity equation are used.