Global solutions to the lagrangian averaged navier-stokes equation in low-regularity besov spaces

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2 Citations (Scopus)

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 H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.

Original languageEnglish
Pages (from-to)697-724
Number of pages28
JournalAdvances in Differential Equations
Volume17
Issue number7-8
StatePublished - 2012
Externally publishedYes

Fingerprint

Besov Spaces
Global Solution
Navier Stokes equations
Navier-Stokes Equations
Regularity
Sobolev spaces
Sobolev Spaces
Interpolation
Interpolate
Approximation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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 H3/4,2(R3) and in the Besov space Bn/2 2,q (Rn). In this paper, we use an interpolation-based method to prove the existence of global solutions to the LANS equation with initial data in B3/p p,q (R3) for any p > n.",
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