【摘要】 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L~q([0,T];L~p(R~4))条件，保证该方程能量守恒.更多还原

【Abstract】 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.更多还原