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The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. (English) Zbl 1026.76004
Summary: We study the equations governing the motion of second-grade fluids in a bounded domain of d , d=2,3, with Navier-slip boundary conditions with and without viscosity (averaged Euler equations). We show global existence and uniqueness of H 3 solutions in dimension two. In dimension three, we obtan local existence of H 3 solutions for arbitrary initial data, and global existence for small initial data and positive viscosity. We close by finding Lyapunov stability conditions for stationary solutions for averaged Euler equations similar to Rayleigh-Arnold stability result for the classical Euler equations.
MSC:
76A05Non-Newtonian fluids
35Q35PDEs in connection with fluid mechanics