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Sibirsk. Mat. Zh., 2017, Volume 58, Number 4, Pages 728–744 (Mi smj2893)  

Well-posedness of a nonstationary axisymmetric hydrodynamic problem with free surface

V. N. Belykh

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: On assuming that the fluid motion is potential, we prove a local existence and uniqueness theorem for a time-analytic solution in an exact mathematical statement. We obtain a rigorous description of the initial stage of the nonstationary motion of an axisymmetric fluid droplet preceding the moment of evolutionary destruction (blow-up) of the free boundary.

Keywords: free boundary, ideal fluid, Cauchy problem, analytic solution.

DOI: https://doi.org/10.17377/smzh.2017.58.402

Full text: PDF file (325 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:4, 564–577

Bibliographic databases:

Document Type: Article
UDC: 517.95+532.22
MSC: 35R30
Received: 24.11.2016

Citation: V. N. Belykh, “Well-posedness of a nonstationary axisymmetric hydrodynamic problem with free surface”, Sibirsk. Mat. Zh., 58:4 (2017), 728–744; Siberian Math. J., 58:4 (2017), 564–577

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