The existence and uniqueness of nonstationary ideal incompressible flow in bounded domains in 𝑅₃

Swann, H. S. G.

doi:10.1090/S0002-9947-1973-0326197-8

The existence and uniqueness of nonstationary ideal incompressible flow in bounded domains in $R_{3}$
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by H. S. G. Swann PDF

Trans. Amer. Math. Soc. 179 (1973), 167-180 Request permission

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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