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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

An existence result for non-Newtonian fluids in non-regular domains

Pages: 255 - 268, Volume 3, Issue 2, June 2010

doi:10.3934/dcdss.2010.3.255       Abstract        Full Text (238.7K)       Related Articles

Lars Diening - Universität Freiburg, Mathematisches Institut, Eckerstr. 1, D-79104 Freiburg, Germany (email)
Michael Růžička - Universität Freiburg, Mathematisches Institut, Eckerstr. 1, D-79104 Freiburg, Germany (email)

Abstract: We show the existence of weak solutions to the steady system describing the motion of certain non-Newtonian fluids in non-regular domains. This generalizes previous results for Lipschitz continuous domains. In the proof we combine a localization of the Lipschitz truncation method with a domain decomposition theorem, which enables to extend results known for nice domains to John domains.

Keywords:  non-Newtonian fluids, electrorheological fluids, John domains, divergence equation, Korn's inequality, Lebesgue and Sobolev spaces with variable exponents, Lipschitz truncation method, domain decomposition, theorem of de Rham.
Mathematics Subject Classification:  35Q35, 35D05, 26D10, 46E30, 35B45.

Received: May 2009;      Published: April 2010.