The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space
By Igor Kukavica, Vlad Vicol. 2010
48 citations recorded by the source corpus.
We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t} \Vert \nabla u(s) \Vert_{L^\infty} ds}$, improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/11fccf8e45f59bd5cb7fb0357e15e26ad53ea1a3
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In Applied Mathematics
- Tak Kwong Wong
- Nader Masmoudi
- Vlad Vicol
- Yasunori Maekawa
- Davdi Gerard-Varet
- Frédéric Rousset
- Peter Constantin
- Pierre Germain
In Mathematical Physics
- Nader Masmoudi
- Tak Kwong Wong
- Yasunori Maekawa
- Vlad Vicol
- Davdi Gerard-Varet
- Pierre Germain
- Sijue Wu
- Marius Paicu
Citations in the corpus
- Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “In full generality, these questions are still open except in the analytic case where (a)-(c) can be proved [27, 26, 16, 15].”