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⋅n=a, 2D(v)n⋅s+αv⋅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 LpLp-bounded vorticity, p∈(2,∞]p∈(2,∞]. To prove the solvability we realize the passage to the limit in Navier–Stokes equations with vanishing viscosity.