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June  2010, 3(2): 255-268. doi: 10.3934/dcdss.2010.3.255

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

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

Received  May 2009 Published  April 2010

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.
Citation: Lars Diening, Michael Růžička. An existence result for non-Newtonian fluids in non-regular domains. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 255-268. doi: 10.3934/dcdss.2010.3.255
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