# zbMATH — the first resource for mathematics

New conditions for local regularity of a suitable weak solution to the Navier-Stokes equation. (English) Zbl 1010.35081
Summary: We formulate conditions which guarantee that a suitable weak solution $$(v,p)$$ to the Navier-Stokes equation (in the sense of L. Caffarelli, R. Kohn and L. Nirenberg [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)]) cannot have a singularity at the point $$(x_0,t_0)\in \mathbb{R}^3\times (0,T)$$. The usual Prodi-Serrin condition on the velocity $$v$$ is substantially replaced by an analogous condition imposed on the negative part $$p_-$$ of the pressure $$p$$.

##### MSC:
 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 35B65 Smoothness and regularity of solutions to PDEs
Zbl 0509.35067
Full Text: