Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Well-posedness results for the Navier-Stokes equations in the rotational framework

Pages: 5143 - 5151, Volume 33, Issue 11/12, November/December 2013      doi:10.3934/dcds.2013.33.5143

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Matthias Hieber - Fachbereich Mathematik, Angewandte Analysis, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany (email)
Sylvie Monniaux - LATP UMR 6632, CMI, Technopôle de Château-Gombert, 39 rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13, France (email)

Abstract: Consider the Navier-Stokes equations in the rotational framework either on $\mathbb{R}^3$ or on open sets $\Omega \subset \mathbb{R}^3$ subject to Dirichlet boundary conditions. This paper discusses recent well-posedness and ill-posedness results for both situations.

Keywords:  Navier-Stokes equations, Coriolis force, Stokes-Coriolis semigroup, Dirichlet boundary conditions, mild solutions.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: January 2012;      Revised: July 2012;      Available Online: May 2013.