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2010, Volume 3, Issue 2: 199-219. Doi: 10.3934/dcdss.2010.3.199
This issue Previous Article Loss of smoothness and energy conserving rough weak solutions for the $3d$ Euler equations Next Article The Dirichlet to Neumann map - An application to the Stokes problem in half space

An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case.

  • 1.

    Dipartimento di Matematica Applicata "U. Dini”, Via F. Buonarroti 1/c, I-56127, Pisa

Received:  January 31, 2009
Revised:  May 31, 2009
Published:  May 2010
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    Abstract
  • We study with elementary tools the stationary 3D Navier-Stokes equations in a flat domain, equipped with Navier (slip without friction) boundary conditions. We prove existence and uniqueness of weak, strong, and very-weak solutions in appropriate Banach spaces and most of the result hold true without restrictions on the size of the data. Results are partially known, but our approach allows us to give rather elementary and self-contained proofs.
    Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D03.

    Citation:
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