Relaxation of Euler equations and hydrodynamic instabilities

Duchon, Jean; Robert, Raoul

doi:10.1090/qam/1162274

Authors: Jean Duchon and Raoul Robert
Journal: Quart. Appl. Math. 50 (1992), 235-255
MSC: Primary 76C05; Secondary 35Q35, 76E99
DOI: https://doi.org/10.1090/qam/1162274
MathSciNet review: MR1162274
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Abstract: We present a relaxed version of incompressible Euler equations that permits foliated flows involving two velocities. These relaxed equations allow a two-phase evolution of some vortex sheets as an alternative to discontinuous solutions of Euler equations. In the case of two perfect fluids of different densities superposed one over the other, we show that this relaxation process yields a linearly well-posed two-phase solution.

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