Remarks on global weak solutions to a two-fluid type model

Remarks on weak solutions for a nonlocal parabolic problem

where Ω is a smooth bounded open subset of RN with regular boundary Γ. In problem (1.1) a and f are both continuous functions, whose properties will be introduced when necessary, l : L2(Ω) → R is a nonlinear form, h ∈ L2(0,T ;H−1(Ω)), and T > 0 is some fixed time. System (1.1) is studied, for instance, in papers of Chipot and Lovat [4] in case f = f (x) depends only on the variable x. In this w...

Weak Solutions for a Fluid-elastic Structure Interaction Model

The purpose of this paper is to study a model coupling an incompressible viscous fluid with an elastic structure in a bounded container. We prove the existence of weak solutions “à la Leray” as long as no collisions occur.

Global Weak Solutions of a Polymer Crystal Growth Model

The aim of this paper is to show the global existence of weak solutions for a moving boundary problem arising in the non-isothermal crystallization of polymers. The main features of our works are (i) the moving interface is shown to be of co-dimension one; (ii)finite Hölder continuous propagation speed yields an intrinsic estimate of finite co-dimension one Hausdorff measure of the moving inter...

Global Existence of Weak Solutions for a Viscous Two-phase Model

The purpose of this paper is to explore a viscous two-phase liquid-gas model relevant for well and pipe flow. Our approach relies on applying suitable modifications of techniques previously used for studying the single-phase isothermal Navier-Stokes equations. A main issue is the introduction of a novel two-phase variant of the potential energy function needed for obtaining fundamental a priori...

Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid