Euler equations with non-homogeneous Navier slip boundary conditions

We consider the flow of an ideal fluid in a 2D bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with non-homogeneous Navier slip boundary conditions. These conditions can be written in the form v center dot n = a, 2D(v)n center dot s + alpha v center dot s = b, where the tensor D(v) is the rate of strain of the fluid's velocity v and (n, s) is the pair formed by the normal and tangent vectors to the boundary. We establish the solvability of this problem for the class of solutions with L-p-bounded vorticity, p is an element of (2, infinity]. To prove the solvability we realize the passage to the limit in Navier-Stokes equations with vanishing viscosity. (c) 2007 Elsevier B.V. All rights reserved.