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Large-frequency global regularity for the incompressible Navier–Stokes equation

Published online by Cambridge University Press:  14 November 2011

Joel D. Avrin
Joel D. Avrin
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, NC 28223-0001, USA
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Abstract

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 903 - 912
Copyright
Copyright © Royal Society of Edinburgh 1999

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