Regularity Criterion Of Incompressible Navier-stokes Equations And Stability Of Leray Weak Solution

This paper mainly studies the regularity of three dimensional incompressible Navier-Stokes Equations and the stability of Leray weak solution.This paper is divided into five chapters,specifically,In chapter 1,we briefly review the research background,relevant definitions,common notations and some important inequalities,and give the main results of this paper.In chapter 2,we investigate the regularity of the solution of three dimensional incompressible NavierStokes Equations.Based on the new estimation methods and techniques,we obtain the improved regularity criterion of ?3u based on the previous research.In chapter 3,we investigate the regularity problem of three dimensional incompressible Navier-Stokes Equations based on geometric type,improve the value range of q in Li[21],and prove the average-in-time bound of the spatial Lq norm of the vorticity can be improved to be a uniform-in-time bound,so that the solution is smooth.In chapter 4,we investigate the stability of the Leray weak solution of the three dimensional incompressible Navier-Stokes Equations,and extend the integrability index q in Dong-jia[22],our conclusion can deal with all possible q,and even obtain the stability result of Leray weak solution in the Besov space of negative canonical index.In chapter 5,we continue to investigate the stability of the Leray weak solution of the three dimensional incompressible Navier-Stokes Equations,and as a result of chapter 4 does not take into account to show that the convergence rate.Therefore,we obtain the optimal upper and lower bounds of the convergence rate of three dimensional incompressible Navier-Stokes Equations under large initial perturbations,so as to describe the stability results more intuitively.