On the two-phase Navier-Stokes equations with surface tension. (English) Zbl 1202.35359
Summary: 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.
MSC:
35R35 | Free boundary problems for PDEs |
35Q30 | Navier-Stokes equations |
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
76D45 | Capillarity (surface tension) for incompressible viscous fluids |
76T10 | Liquid-gas two-phase flows, bubbly flows |