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 …

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 …

In this paper we investigate vector-valued parabolic initial boundary value problems of
relaxation type. Typical examples for such boundary conditions are dynamic boundary …

The two-phase free boundary value problem for the isothermal Navier–Stokes system is
studied for general bounded geometries in absence of phase transitions, external forces and …

In this paper, we proved the generalized resolvent estimate and the maximal Lp-Lq
regularity of the Stokes equation with first order boundary condition in the half-space, which …

In the present work, we consider the evolution of two fluids separated by a sharp interface in
the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our …

In these lecture notes, we study free boundary problems for the Navier–Stokes equations
with and without surface tension. The local well-posedness, global well-posedness, and …

Abstract Consider the (simplified) Leslie–Ericksen model for the flow of nematic liquid
crystals in a bounded domain Ω⊂ R n for n> 1. This article develops a complete dynamic …

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky
porous structures are of critical importance for the evaluation of oil or gas recovery and …

The two-phase free boundary problem with surface tension and downforce gravity for the
Navier-Stokes system is considered in a situation where the initial interface is close to …