Spiegelgasse 5, Seminarraum 05.002

## Seminar Analysis and Mathematical Physics: Mickaël Latocca (Université d'Évry)

**Regularity of the Pressure in the Incompressible Euler Equation in a Bounded Domain**

In an incompressible fluid, the pressure is governed by the elliptic equation $-\Delta p = \div \div u \otimes u$ and a Neuman-type boundary condition, where $u$ stands for the divergence-free velocity vector field. The main goal of this talk is to explain why one expects that $p$ has Double Hölder regularity (with respect to that of $u$) and how one can rigourously prove such a fact in a bounded domain. The results presented in this talk were obtained in collaboation with Luigi De Rosa (Basel) and Giorgio Stefani (SISSA).

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