Continuous Approximations of Goldshtik's Model

We consider continuous approximations to the Goldshtik problem for separated flows in an incompressible fluid. An approximated problem is obtained from the initial problem by small perturbations of the spectral parameter (vorticity) and by approximating the discontinuous nonlinearity continuously in the phase variable. Under certain conditions, using a variational method, we prove the convergence of solutions of the approximating problems to the solution of the original problem.