This article is cited in 1 paper

Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions

A. E. Mamontov^a, M. I. Uvarovskaya<sup>b

a</sup> 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.

UDC: 517.95

Received: 11.07.2007

 English version: Journal of Applied Mechanics and Technical Physics, 2008, 49:4, 629–641

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