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arXiv · 1911.11609

Poles and branch cuts in free surface hydrodynamics

P. M. Lushnikov·V. E. Zakharov
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Abstract

We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics though the time-dependent conformal mapping $z=x+iy=z(w,t)$ of the lower complex half plane of the conformal variable $w$ into the area occupied by fluid. We established the exact results on the existence vs. nonexistence of the pole and power law branch point solutions for $1/z_w$ and the complex velocity. We also proved the nonexistence of the time-dependent rational solution of that problem for the second and the first order moving pole.

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P. M. Lushnikov, V. E. Zakharov. 2019-11-24. Poles and branch cuts in free surface hydrodynamics. https://doi.org/10.1007/s42286-020-00040-y

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