Vol. 262, No. 1, 2013

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ISSN: 0030-8730
On existence of a classical solution to a generalized Kelvin–Voigt model

Miroslav Bulíček, Petr Kaplický and Mark Steinhauer

Vol. 262 (2013), No. 1, 11–33
Abstract

We consider a two-dimensional generalized Kelvin–Voigt model describing a motion of a compressible viscoelastic body. We establish the existence of a unique classical solution to such a model in the spatially periodic setting. The proof is based on Meyers’ higher integrability estimates that guarantee the Hölder continuity of the gradient of velocity and displacement.

Keywords
Kelvin–Voigt model, regularity, classical solution, large-data and long-time
Mathematical Subject Classification 2000
Primary: 35B65, 35Q74, 74D10
Milestones
Received: 19 September 2011
Revised: 8 November 2012
Accepted: 13 November 2012
Published: 27 March 2013
Authors
Miroslav Bulíček
Mathematical Institute, Faculty of Mathematics and Physics
Charles University in Prague
186 75 Praha 8
Czech Republic
Petr Kaplický
Department of Mathematical Analysis, Faculty of Mathematics and Physics
Charles University in Prague
186 75 Praha 8
Czech Republic
Mark Steinhauer
Mathematical Institute
University of Koblenz-Landau
Campus Koblenz
56070 Koblenz
Germany