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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2008, Volume 49, Issue 4, Pages 130–145
(Mi pmtf1934)
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This article is cited in 1 scientific paper (total in 1 paper)
Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions
A. E. Mamontova, M. I. Uvarovskayab a Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Institute of Mathematics and Informatics, Ammosov Yakutsk State University, Yakutsk, 677016, Russia
Abstract:
The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical interpretation of these results.
Keywords:
Euler equations, ideal incompressible fluid, nonstationary flows, generalized solutions, Orlicz spaces, Gronwall lemma.
Received: 11.07.2007
Citation:
A. E. Mamontov, M. I. Uvarovskaya, “Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions”, Prikl. Mekh. Tekh. Fiz., 49:4 (2008), 130–145; J. Appl. Mech. Tech. Phys., 49:4 (2008), 629–641
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https://www.mathnet.ru/eng/pmtf1934 https://www.mathnet.ru/eng/pmtf/v49/i4/p130
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