Advances in Differential Equations

Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces

Nathan Pennington

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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 $p>n$.

Article information

Source
Adv. Differential Equations Volume 17, Number 7/8 (2012), 697-724.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355702973

Mathematical Reviews number (MathSciNet)
MR2963801

Zentralblatt MATH identifier
1254.76057

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 35A02: Uniqueness problems: global uniqueness, local uniqueness, non- uniqueness 35K58: Semilinear parabolic equations

Citation

Pennington, Nathan. Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces. Adv. Differential Equations 17 (2012), no. 7/8, 697--724. https://projecteuclid.org/euclid.ade/1355702973.


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