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Solenoidal Lipschitz truncation and applications in fluid mechanics. (English) Zbl 1245.35080

Summary: 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 Bogovskiĭ operators does not work.
Furthermore, we extend the concept of almost A-harmonicity to the fluid context in the pressure free formulation.

MSC:

35Q30 Navier-Stokes equations
35J60 Nonlinear elliptic equations
35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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