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July/August 2012 Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces
Nathan Pennington
Adv. Differential Equations 17(7/8): 697-724 (July/August 2012).

Abstract

The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space $H^{3/4,2}(\mathbb{R}^3)$ and in the Besov space $B^{n/2}_{2,q}(\mathbb{R}^n)$. In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in $B^{3/p}_{p,q}(\mathbb{R}^3)$ for any $p>n$.

Citation

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Nathan Pennington. "Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces." Adv. Differential Equations 17 (7/8) 697 - 724, July/August 2012.

Information

Published: July/August 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1254.76057
MathSciNet: MR2963801

Subjects:
Primary: 35A02, 35K58, 76D05

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.17 • No. 7/8 • July/August 2012
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