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On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids


Authors: M. Bildhauer, M. Fuchs and X. Zhong
Original publication: Algebra i Analiz, tom 18 (2006), nomer 2.
Journal: St. Petersburg Math. J. 18 (2007), 183-199
MSC (2000): Primary 76M30, 76B03, 35Q35
DOI: https://doi.org/10.1090/S1061-0022-07-00948-X
Published electronically: March 16, 2007
MathSciNet review: 2244934
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Abstract | References | Similar Articles | Additional Information

Abstract: A system of nonautonomous partial differential equations describing the steady flow of an incompressible fluid is considered. The existence of a strong solution of that system is proved under suitable assumptions on the data. In the 2D-case this solution turns out to be of class $ C^{1,\alpha}$.


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Additional Information

M. Bildhauer
Affiliation: Department of Mathematics, Saarland University, P.O. Box 15 11 50, D-66041 Saarbrücken, Germany
Email: bibi@math.uni-sb.de

M. Fuchs
Affiliation: Department of Mathematics, Saarland University, P.O. Box 15 11 50, D-66041 Saarbrücken, Germany
Email: fuchs@math.uni-sb.de

X. Zhong
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40014 University of Jyväskylä, Finland
Email: zhong@maths.jyu.fi

DOI: https://doi.org/10.1090/S1061-0022-07-00948-X
Keywords: Generalized Newtonian fluids, anisotropic dissipative potentials, existence and regularity of solutions
Received by editor(s): October 31, 2005
Published electronically: March 16, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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