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June 2012 Leray's Inequality for Fluid Flow in Symmetric Multi-connected Two-dimensional Domains
Reinhard FARWIG, Hiroko MORIMOTO
Tokyo J. Math. 35(1): 63-70 (June 2012). DOI: 10.3836/tjm/1342701344

Abstract

We consider the stationary Navier-Stokes equations with nonhomogeneous boundary condition in a domain with several boundary components. If the boundary value satisfies only the necessary flux condition (GOC), Leray's inequality does not holds true in general and we cannot prove the existence of a solution. But for a 2-D domain which is symmetric with respect to a line and where the data is also symmetric, C. Amick showed the existence of solutions by reduction to absurdity; later H. Fujita proved Leray-Fujita's inequality and hence the existence of symmetric solutions. In this paper we give a new short proof of Leray-Fujita's inequality and hence a proof of the existence of weak solutions.

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Reinhard FARWIG. Hiroko MORIMOTO. "Leray's Inequality for Fluid Flow in Symmetric Multi-connected Two-dimensional Domains." Tokyo J. Math. 35 (1) 63 - 70, June 2012. https://doi.org/10.3836/tjm/1342701344

Information

Published: June 2012
First available in Project Euclid: 19 July 2012

zbMATH: 1256.35053
MathSciNet: MR2977445
Digital Object Identifier: 10.3836/tjm/1342701344

Subjects:
Primary: 35Q30
Secondary: 76D05

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 1 • June 2012
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