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Incompressible Viscous Flows in Borderline Besov Spaces

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Abstract

We establish two new estimates for a transport-diffusion equation. As an application we treat the problem of global persistence of the Besov regularity \(B_{p,1}^{\frac{2}{p}+1},\) with \(p \in ]2,+\infty]\) , for the two-dimensional Navier–Stokes equations with uniform bounds on the viscosity. We provide also an inviscid global result.

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Authors and Affiliations

  1. IRMAR, Universitè de Rennes 1, Campus de Beaulieu, 35042, Rennes, France

    Taoufik Hmidi & Sahbi Keraani

Authors
  1. Taoufik Hmidi
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  2. Sahbi Keraani
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Correspondence to Taoufik Hmidi.

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Communicated by Y. Brenier

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Hmidi, T., Keraani, S. Incompressible Viscous Flows in Borderline Besov Spaces. Arch Rational Mech Anal 189, 283–300 (2008). https://doi.org/10.1007/s00205-008-0115-7

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  • DOI: https://doi.org/10.1007/s00205-008-0115-7

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