## Zden\v ek Skal\'ak

*Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations *

Comment.Math.Univ.Carolinae 43,4 (2002) 619-639. **Abstract:**In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin's type on velocity ${\bold v}$ and pressure $p$ under which $({\bold x}_0,t_0)\in \Omega \times (0,T)$ is a regular point of ${\bold v}$. The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex $({\bold x}_0,t_0)$ and the axis parallel with the $t$-axis.

**Keywords:** Navier-Stokes equations, suitable weak solutions, local regularity

**AMS Subject Classification:** 35Q10, 35B65

PDF