Regularity Criteria For Navier-Stokes Equations

In this paper,we consider whether the incompressible Navier-Stokes equations can provide regularity criteria for the combination of velocity,velocity gradient,pressure gradient,and curl components.The details are as follows.The first chapter which briefly introduces the research background and research progress of NavierStokes equations,the research contents,methods and innovations of this paper.In the second chapter,we give some inequalities and their proofs which need to be used in the paper.In the third chapter,we consider the cauchy problem of Navier-Stokes equations of general dimension,and establishes several new regularity criteria for partial components.In the fourth chapter,we consider the H (?)lder-type criterion of vorticity direction for three-dimensional incompressible Navier-Stokes equations;We also consider the Berselli-Cordoba-type criterion for threedimensional incompressible Navier-Stokes systems,and extends Lipschitz continuity of vorticity dierction relative to space to anisotropic H (?)lder continuity.