APDE Seminar @UPV/EHU: Nonlinear fluids and Lipschitz truncations

Abstract

We provide existence of very weak solutions and a-priori estimates for steady flows of non-Newtonian fluids of Stokes and Navier-Stokes type when the right-hand sides are not in the natural existence class. This includes stress laws that depend non-linearly on the shear rate of the fluid like power-law fluids. To obtain the a-priori estimates we make use of a refined solenoidal Lipschitz truncation that preserves zero boundary values.

We provide also estimates in (Muckenhoupt) weighted spaces which permit us to regain a duality pairing, which than can be used to prove existence of solutions. Joint work with Sebastian Schwarzacher (Uppsala and Prague).