Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1910-1942 |
| Number of pages | 33 |
| Journal | Journal of Differential Equations |
| Volume | 253 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 15 Sept 2012 |
Keywords
- Solenoidal Lipschitz truncation
- Divergence free truncation
- Navier-Stokes
- Generalized Newtonian fluids
- Prandtl-Eyring fluid
- A-harmonic approximation
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