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Ad hoc closed form solutions of the two-dimensional nonlinear steady small perturbation equation in fluid mechanics. (English) Zbl 0837.76038

Summary: Making use of convenient ad hoc assumptions we construct closed-form solutions of the nonlinear two-dimensional irrotational steady small perturbation equation appearing in fluid mechanics. The methodologies developed succeed in giving the above solutions expressed in the form of fewer arbitrary functions than needed for general solutions. As an application, we specify the above-mentioned solutions in the case of the simplified nonlinear transonic equation governing the boundary value problem of a two-dimensional flow past a wave shaped wall.

MSC:

76H05 Transonic flows
35B20 Perturbations in context of PDEs
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