An existence result for non-Newtonian fluids in non-regular domains
Lars Diening, Michael Růžička · Discrete and Continuous Dynamical Systems - S · 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.