We extend the Lipschitz truncation method to the setting of solenoidal functions. In particular, we approximate a solenoidal Sobolev function by a solenoidal Lipschitz function which differs from the original function only on a small set.
Our main application is the existence of weak solutions to the two-dimensional Prandtl-Eyring fluid model which has almost linear growth. In this situation a correction via Bogovskii operators does not work.
Furthermore, we extend the concept of almost A-harmonicity to the fluid context in the pressure free formulation. (C) 2012 Elsevier Inc. All rights reserved.
- Solenoidal Lipschitz truncation
- Divergence free truncation
- Generalized Newtonian fluids
- Prandtl-Eyring fluid
- A-harmonic approximation
- GENERAL BOUNDARY CONDITIONS