三维非均匀不可压缩Navier-Stokes方程弱解的存在性

On the existence of weak solutions to 3D inhomogeneous incompressible Navier- Stokes equations

首先构造非均匀不可压缩Navier-Stokes方程满足正则化初值的近似解,并对近似解作一致估计,然后将近似解过渡到极限,从而证明了方程存在满足局部能量不等式的弱解.

Firstly, approximated solutions satisfying the regularized initial data are constructed, and the uniform estimate of these approximated solutions was deduced. Then the existence of weak solution to 3 D inhomogeneous incompressible Navier- Stokes equations satisfying the local energy inequality is obtained by passing to the limit.