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An existence theorem for a free surface flow problem with open boundaries. (English) Zbl 0767.35061

The author proves the existence and uniqueness results for a flow problem which involves a free surface terminating at inflow and outflow boundaries. The flows under consideration are small perturbations of uniform flow with a flat surface.
Both steady flows and initial value problems are investigated. The smoothness of solutions is limited by the singularity at the corner between the free surface and the in flow boundary. The technique of the proof is basically to derive coercivity estimates for the linearized problem and then use a contraction argument for the nonlinear problem.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35G25 Initial value problems for nonlinear higher-order PDEs
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