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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 285 - 303, Volume 29, Issue 1, January 2011      doi:10.3934/dcds.2011.29.285

 
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Igor Kukavica - Department of Mathematics, University of Southern California, 3620 South Vermont Ave., Los Angeles, CA 90089-2532, United States (email)
Vlad C. Vicol - Department of Mathematics, University of Southern California, 3620 South Vermont Ave., Los Angeles, CA 90089-2532, United States (email)

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.

Keywords:  Euler equations, analyticity radius, Gevrey class.
Mathematics Subject Classification:  Primary: 76B03; Secondary: 35L60.

Received: October 2009;      Revised: May 2010;      Available Online: September 2010.

 References