Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Abstract: Given any solution $u$ of the Euler equations which is assumed to have some regularity in space - in terms of Besov norms, natural in this context - we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure $p$ is twice as regular as $u$. This generalizes a recent result by Isett 16, which covers the case of H\"older spaces.