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

Lars Diening; Michael Růžička

doi:10.3934/dcdss.2010.3.255

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2010, Volume 3, Issue 2: 255-268. Doi: 10.3934/dcdss.2010.3.255

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

Lars Diening^1, and
Michael Růžička^1,

1.
Universität Freiburg, Mathematisches Institut, Eckerstr. 1, D-79104 Freiburg

Received: April 30, 2009

Published: May 2010

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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.

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