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 ε2. Assuming the RayleighTaylor sign condition, and ρ- ≤ ε3/2, 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, ρ- → 0.
Original language | English (US) |
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Pages (from-to) | 347-373 |
Number of pages | 27 |
Journal | Journal of Hyperbolic Differential Equations |
Volume | 8 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2011 |
All Science Journal Classification (ASJC) codes
- Analysis
- General Mathematics
Keywords
- Euler equations
- surface tension
- vortex-sheet problem