The domain of analyticity of solutions to the three-dimensional Euler equations in a half space

Igor Kukavica; Vlad C. Vicol

doi:10.3934/dcds.2011.29.285

Article Contents

2011, Volume 29, Issue 1: 285-303. Doi: 10.3934/dcds.2011.29.285

This issue Previous Article Preservation of homoclinic orbits under discretization of delay differential equations Next Article Non-integrability of the collinear three-body problem

The domain of analyticity of solutions to the three-dimensional Euler equations in a half space

Igor Kukavica^1, and
Vlad C. Vicol^1,

1.
Department of Mathematics, University of Southern California, 3620 South Vermont Ave., Los Angeles, CA 90089-2532

Received: September 30, 2009

Revised: April 30, 2010

Published: December 2010

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Abstract

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} $||$ \nabla u(s) $||_L^∞ 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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Mathematics Subject Classification: Primary: 76B03; Secondary: 35L60.

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