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Continuous approximations of Gol’dshtik’s model. (English. Russian original) Zbl 1198.35199

Math. Notes 87, No. 2, 244-247 (2010); translation from Mat. Zametki 87, No. 2, 262-266 (2010); erratum Math. Notes 87, No. 3, 453 (2010).
Summary: We consider continuous approximations to the Gol’dshtik 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A35 Theoretical approximation in context of PDEs
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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References:

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