On the two-phase Navier-Stokes equations with surface tension

Abstract

The two-phase free boundary problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. By means of Lp-maximal regularity of the underlying linear problem we show local well-posedness of the problem, and prove that the solution, in particular the interface, becomes instantaneously real analytic. © European Mathematical Society 2010.