We prove the existence of an obstacle lying on the bottom of an infinite channel inducing a surface on the upper bound of the fluid domain. This problem is the inverse of the free-surface problem flow which has been studied by several authors. We use the implicit function theorem to establish the existence of the solution of the problem. γ b the domain occupied by the fluid, where b is the equation of the obstacle and γ is the perturbation of the upper bound. We set
1)Abstract and Applied Analysis
A theoretical method based on the hodograph transformation is presented to solve the problem of an irrotational and steady flow of an inviscid and incompressible fluid, over a two-dimensional obstacle lying on the bottom of a channel. The suggested method for the solution of the fully non-linear problem is presented for a super-critical flow (Froude number Fr > 1). The results obtained are based on those established in [6] and [7].
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