Short-time structural stability of compressible vortex sheets with surface tension (Q338090)

The author studies two inviscid fluid flowing past each other, when surface tension produces a force across the interface, balanced by the pressure jump. This vortex-sheet configuration is modelled by the compressible Euler equations with a general equation of state for the pressure, density and entropy. The main result is the local in time existence of a solution together with its stability. The strategy of the proof consists in a regularization with an artificial viscosity which allows the author to linearize the system and obtain a collection of transport equations for the entropy, pressure and curl.