| Abstract: |
| As is well known, the regularity of the weak solutions of the Navier-Stokes equations (NSE) is still an open problem. In our talk we present a survey of some recent results on the conditional regularity of solutions to NSE in the whole three-dimensional space and focus maily on the Prodi-Serrin conditions imposed only on $\nabla u_3$, $\partial_3 u$ and $\partial_1 u_3$, where $u=(u_1,u_2,u_3)$ stands for the velocity. We are especially interested in optimal results. |
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