四维不可压缩Navier-Stokes方程的能量守恒

Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

研究了四维不可压缩Navier-Stokes方程的能量守恒,当该方程的Leray-Hopf弱解(适当弱解)存在维数小于4的奇异集时,基于Wu在文章中关于四维不可压缩Navier-Stokes方程的部分正则性结果,得到了四维空间中Lq([0,T];Lp(R4))条件,保证该方程能量守恒.

The energy conservation of 4D incompressible Navier-Stokes equations was studied.In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution(suitable weak solution),the L q([0,T];L p(R 4))condition in the 4D space was obtained based on Wu’s partial regularity results about the 4D incompressible Navier-Stokes equations,to ensure the energy conservation.