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Équation de Monge-Ampère et écoulements incompressibles bidimensionnels. (The Monge-Ampère equation and two-dimensional incompressible flows). (French) Zbl 0704.76026

Summary: We show that the solutions of the two-dimensional Navier-Stokes equation on a domain V are determined by the knowledge of the pressure Laplacian on V and the knowledge of the stream function on \(\partial V\) via a Monge-Ampère equation. A case of uniqueness is studied and applications to coherent structures analysis are developed.

MSC:

76F99 Turbulence
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