Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

We prove that the profile of a periodic traveling wave propagating at the surface of water
above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the …

It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw
models. This implies, in particular, existence and uniqueness of classical solutions for a …

CLASSICAL SOLUTIONS OF MULTIDIMENSIONAL HELE–SHAW MODELS 1. The problem.
We are concerned with a class of moving boundary prob Page 1 CLASSICAL SOLUTIONS OF …

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 …

We provide existence of a unique smooth solution for a class of one-and two-phase Stefan
problems with Gibbs-Thomson correction in arbitrary space dimensions. In addition, it is …

The Mullins–Sekerka model is a nonlocal evolution model for hypersurfaces, which arises
as a singular limit for the Cahn–Hilliard equation. We show that classical solutions exist …

We consider the Muskat problem describing the motion of two unbounded immiscible fluid
layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first …

Mathematische Annalen Page 1 Math. Ann. (2007) 338:703–755 DOI 10.1007/s00208-007-0094-2
Mathematische Annalen Existence of analytic solutions for the classical Stefan problem Jan …

We consider the motion of two superposed immiscible, viscous, incompressible, capillary
fluids that are separated by a sharp interface which needs to be determined as part of the …