ON THE LIMIT AS THE SURFACE TENSION AND DENSITY RATIO TEND TO ZERO FOR THE TWO-PHASE EULER EQUATIONS

摘要

We consider the free boundary motion of two perfect incompressible fluidsnwith different densities ρ+ and ρ−, separated by a surface of discontinuity along which thenpressure experiences a jump proportional to the mean curvature by a factor ε2. Assumingnthe Rayleigh–Taylor sign condition, and ρ− ≤ ε3/2, we prove energy estimates uniform innρ− and ε. As a consequence, we obtain convergence of solutions of the interface problemnto solutions of the free boundary Euler equations in vacuum without surface tension asnε, ρ− → 0.