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Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
Nonlinearity ( IF 1.7 ) Pub Date : 2020-08-03 , DOI: 10.1088/1361-6544/ab8fb5
Maria Colombo , Luigi De Rosa , Luigi Forcella

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.

中文翻译:

不可压缩欧拉方程通过插值法粗解的正则性结果

给定欧拉方程的任何解 $u$,假设它在空间中具有某种规律性 - 根据 Besov 范数,在这种情况下是自然的 - 我们通过插值方法表明它在时间上具有相应的规律性,并且相关的压力 $ p$ 是 $u$ 的两倍。这概括了 Isett [16] 的最近结果(另见 Colombo 和 De Rosa [8]),该结果涵盖了 H\"旧空间的情况。
更新日期:2020-08-03
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