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Solutions in Lebesgue spaces of the Navier-Stokes equations with dynamic boundary conditions

Published online by Cambridge University Press:  14 November 2011

Marié Grobbelaar-Van Dalsen  and
Niko Sauer
Marié Grobbelaar-Van Dalsen
Affiliation:
Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, PO Box 392, Pretoria 0001, South Africa
Niko Sauer
Affiliation:
Faculty of Science, Pretoria University, Pretoria 0002, South Africa
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Synopsis

This paper, although self-contained, is a continuation of the work done in [8], where the motion of a viscous, incompressible fluid is considered in conjunction with the rotation of a rigid body which is immersed in the fluid. The resulting mathematical model is a Navier-Stokes problem with dynamic boundary conditions. In [8] a unique L2,3 solution is constructed under certain regularity assumptions on the initial states. In this paper we consider the Navier-Stokes problem with dynamic boundary conditions in the Lebesgue spaces Lr,3 (3<r<∞) and prove the existence of a unique solution, local in time, without imposing any regularity conditions on the initial states.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 4 , 1993 , pp. 745 - 761
Copyright
Copyright © Royal Society of Edinburgh 1993

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