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Free surface flow over an obstacle. Theoretical study of the fluvial case. (English) Zbl 0998.35068

This paper is devoted to a free boundary value problem for harmonic functions in a strip-like domain. Free boundary condition is the Bernoulli equation. This statement corresponds to a steady flow of an ideal fluid over an obstacle lying on the bottom of a stream. The main result concerns existence and uniqueness of the solution for a sufficiently small Froude number \(F=u_0/\sqrt{gy_0}\) of the flow. Here \(u_0\) is the value of velocity, \(g\) is the downward acceleration due to the gravity and \(y_0\) is the height of a channel at infinity.

MSC:

35R35 Free boundary problems for PDEs
35Q35 PDEs in connection with fluid mechanics
76D27 Other free boundary flows; Hele-Shaw flows
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