Busuioc, Adriana Valentina; Ratiu, Tudor S. The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. (English) Zbl 1026.76004 Nonlinearity 16, No. 3, 1119-1149 (2003). Summary: We study the equations governing the motion of second-grade fluids in a bounded domain of \(\mathbb{R}^d\), \(d=2,3\), 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. Cited in 45 Documents MSC: 76A05 Non-Newtonian fluids 35Q35 PDEs in connection with fluid mechanics Keywords:averaged Euler equations; second-grade fluids; Navier-slip boundary conditions; global existence; uniqueness; local existence; Lyapunov stability conditions PDFBibTeX XMLCite \textit{A. V. Busuioc} and \textit{T. S. Ratiu}, Nonlinearity 16, No. 3, 1119--1149 (2003; Zbl 1026.76004) Full Text: DOI Link