Existence of local suitable weak solutions to the Navier-Stokes equations for initial data in $L_{\mathrm{loc}}^2({\mathbb{R}}^3)$

Dongho Chae, Joerg Wof

We consider the Navier-Stokes equations in ${\mathbb{R}}^3$ subject to the initial condition with initial velocity field in $L_{\mathrm{loc}}^2({\mathbb{R}}^3)$ such that $\limsup_{R \to…