三维不可压Navier-Stokes方程弱解正则准则

Regularity Criterion for Weak Solutions of 3D Incompressible Navier-Stokes Equations

考虑在三维情况下不可压的Navier-Stokes方程弱解的正则性,在建立弱解正则性准则时,主要工作是扩大弱解所满足的函数积分空间.在此使用了Hölder不等式、Young不等式及Sobolev嵌入技术等,扩大了弱解一阶偏导数∂3u所属的积分空间,当∂3u∈L^p(0,T;Lq(R^3))且2/p+3/q=46/25+3/25q,31/8≤q≤∞时,或者当∂3u∈L^p(0,T;Lq(R^3))且2/p+3/q=22/13+3/13q,19/8≤q≤∞时,三维不可压Navier-Stokes方程弱解在(0,T]上是正则的.

This paper considers the regularity of weak solutions for incompressible Navier-Stokes equations in 3D cases.When establishing a weak solution rule of thumb,The main job is to expand the function integration space that the weak solution satisfies.Here,Hölder inequalities,Yuong inequalities,etc.and Sobolev embedding techniques are used to expand the integral space to which the weak solution first-order partial derivative3u belongs.When∂3u∈L^p(0,T;Lq(R^3))and 2/p+3/q=46/25+3/25q,31/8≤q≤∞,or when∂3u∈L^p(0,T;Lq(R^3))and 2/p+3/q=22/13+3/13q,19/8≤q≤∞,The weak solution of three-dimensional incompressible of the Navier-Stokes equation is regular on(0,T].