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arXiv · 1910.00902

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

Maria Colombo·Luigi De Rosa·Luigi Forcella
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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] (see also Colombo and De Rosa [8]), which covers the case of H\"older spaces.

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Maria Colombo, Luigi De Rosa, Luigi Forcella. 2019-10-02. Regularity results for rough solutions of the incompressible Euler equations via interpolation methods. https://doi.org/10.1088/1361-6544/ab8fb5

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