The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space

Details The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space

2010-07-13

arxiv.org/abs/1007.2011v1

Mathematics

Analysis of PDEs

To appear in DCDS-A

Scientific paper

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.

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