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Exactly integrable dynamics of interface between ideal fluid and light viscous fluid. (English) Zbl 1209.37103

Summary: It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between normal velocity and pressure at interface. Surface elevation and velocity potential of ideal fluid are determined from two complex Burgers equations corresponding to analytical continuation of velocity potential at the interface into upper and lower complex half planes, respectively. The interface loses its smoothness if complex singularities (poles) reach the interface.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76D07 Stokes and related (Oseen, etc.) flows
35Q55 NLS equations (nonlinear Schrödinger equations)
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References:

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