A local smoothness criterion for solutions of the 3D Navier-Stokes equations
A local smoothness criterion for solutions of the 3D Navier-Stokes equations
We consider the three-dimensional Navier–Stokes equations on the whole space \mathbb{R}^3 and on the three-dimensional torus \mathbb{T}^3 . We give a simple proof of the local existence of (finite energy) solutions in L^3 for initial data u_0\in L^2\cap L^3 , based on energy estimates and regularisation of the initial data …