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

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

2009-08-23

arxiv.org/abs/0908.3327v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

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 $L_p$-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.

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