Geodesic
A~new class of exact solutions in the~planar nonstationary problem of motion of a~fluid with a~free boundary
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 393-402

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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.
Keywords: ideal incompressible fluid, unsteady planar flow with a free boundary, complex velocity, Hopf equation.
Mots-clés : exact solution 
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     author = {E. N. Zhuravleva and N. M. Zubarev and O. V. Zubareva and E. A. Karabut},
     title = {A~new class of exact solutions in the~planar nonstationary problem of motion of a~fluid with a~free boundary},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {393--402},
     publisher = {mathdoc},
     volume = {202},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a5/}
}
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E. N. Zhuravleva; N. M. Zubarev; O. V. Zubareva; E. A. Karabut. A~new class of exact solutions in the~planar nonstationary problem of motion of a~fluid with a~free boundary. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 393-402. http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a5/