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Transactions of the American Mathematical Society

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The existence and uniqueness of nonstationary ideal incompressible flow in bounded domains in $ R\sb{3}$


Author: H. S. G. Swann
Journal: Trans. Amer. Math. Soc. 179 (1973), 167-180
MSC: Primary 35Q99
DOI: https://doi.org/10.1090/S0002-9947-1973-0326197-8
MathSciNet review: 0326197
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Abstract: It is shown here that the mixed initial-boundary value problem for the Euler equations for ideal flow in bounded domains of $ {R_3}$ has a unique solution for a small time interval. The existence of a solution is shown by converting the equations to an equivalent system involving the vorticity and applying Schauder's fixed point theorem to an appropriate mapping.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0326197-8
Keywords: Nonstationary ideal flow, Euler equations
Article copyright: © Copyright 1973 American Mathematical Society

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