We are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

中文翻译：

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研究无旋周期性重力水波的另一种方法

我们在这里关注的是非线性无旋重力水波问题的分析，其中自由表面位于以平床为边界的水流上方。我们采用了一种新的公式，该公式涉及一个包含压力项的表达式（称为流动力），因此有可能处理复杂的表面动态边界条件。所提出的公式既不需要自由表面的图形假设，也不需要没有停滞点。通过这种替代方法，我们证明了具有固定流动力和更宽松假设的水波问题解的局部曲线的存在。