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.
All Science Journal Classification (ASJC) codes
- Euler equations
- surface tension
- vortex-sheet problem