The Lagrangian Averaged Navier-Stokes equation with rough data in Sobolev spaces

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Abstract

The Lagrangian Averaged Navier-Stokes equation is a recently derived approximation to the Navier-Stokes equation. In this article we prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Sobolev spaces Ws,p(Rn) for 12-based Sobolev spaces, we obtain global existence results. More specifically, we achieve local existence with initial data in the Sobolev space Hn/2p,p(Rn). For initial data in H3/4,2(R3), we obtain global existence, improving on previous global existence results, which required data in H3,2(R3).

Original languageEnglish
Pages (from-to)72-88
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume403
Issue number1
DOIs
Publication statusPublished - Jul 1 2013
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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