Prandtl-Eyring fluids in 2D by means of solenoidal Lipschitz truncation
نویسندگان
چکیده
We prove the existence of weak solutions with homogeneous boundary data for the following equations of Navier-Stokes type equations divσ + f = ∇π + (∇u)u, where u : R ⊃ Ω → R is the velocity field satisfying div u = 0 and f : Ω→ R and π : Ω→ R are the external volume forces resp. the pressure. In order to model the behaviour of Prandtl-Eyring fluids we assume the validity of the stress-strain relation σ = DW (ε(u)), W (ε) = |ε| ln(1 + |ε|). The crucial tool in our approach is a solenoidal Lipschitz truncation. MSC (2000): 76 B 03, 35 D 05, 35 J 60.
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