result for non-Newtonian fluids in non-regular domains
Lars Diening - 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.
Received: May 2009; Published: April 2010.