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arXiv · 0912.3296

On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations

Fabio Pusateri
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Abstract

We consider the free-boundary motion of two perfect incompressible fluids with different densities $ρ_+$ and $ρ_-$, separated by a surface of discontinuity along which the pressure experiences a jump proportional to the mean curvature by a factor $ε^2$. Assuming the Raileigh-Taylor sign condition and $ρ_- \leq ε^{3/2}$ we prove energy estimates uniform in $ρ_-$ and $ε$. As a consequence we obtain convergence of solutions of the interface problem to solutions of the free-boundary Euler equations in vacuum without surface tension as $ε$ and $ρ_-$ tend to zero.

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Fabio Pusateri. 2011-03-06. On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations. https://arxiv.org/abs/0912.3296

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