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The motion of a fluid in an open channel. (English) Zbl 1105.35073

The author considers a free boundary problem for the Navier-Stokes equations describing the oscillations of a viscous, incompressible fluid contained in an uncovered 3D rectangular channel. Some existence results are presented for the linearized and nonlinear version of the problem. The qualitative behaviour of periodic solutions is studied with the help of the spectral analysis of an associated linear system and the Hopf bifurcation theorem.

MSC:

35Q30 Navier-Stokes equations
76D27 Other free boundary flows; Hele-Shaw flows
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References:

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