A new class of exact solutions in the planar nonstationary problem of motion of a fluid with a free boundary

E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

We consider the classical problem of potential unsteady flow of an ideal incompressible fluid with a free boundary. It was previously discovered that in the absence of external forces and capillarity, a wide class of exact solutions of the problem can be described by the Hopf equation for a complex velocity. We here obtain a new class of solutions described by the Hopf equation for a quantity that is the inverse of the complex velocity. These solutions describe the evolution of two-dimensional perturbations of the free boundary in compression or expansion of a circular cavity (in the unperturbed state) in the fluid.

Язык оригиналаанглийский
Страницы (с-по)344-351
Число страниц8
ЖурналTheoretical and Mathematical Physics(Russian Federation)
Том202
Номер выпуска3
DOI
СостояниеОпубликовано - мар 2020

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