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

Global weak solution to the viscous two-phase model with finite energy

In this paper, we prove the existence of global weak solutions to the compressible NavierStokes equations when the pressure law is in two variables. The method is based on the Lions argument and the Feireisl-Novotny-Petzeltova method. The main contribution of this paper is to develop a new argument for handling a nonlinear pressure law P (ρ, n) = ρ + n where ρ, n satisfy the mass equations. Thi...

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

Existence of Weak Solutions for a Non-classical Sharp Interface Model for a Two-phase Flow of Viscous, Incompressible Fluids

Abstract. We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier–Stokes and Mullins–Sekerka type parts that coincides with the asymptotic limit of a diffuse int...

Global Well-Posedness and Finite-Dimensional Global Attractor for a 3-D Planetary Geostrophic Viscous Model

In this paper we consider a three-dimensional planetary geostrophic viscous model of the gyre-scale mid-latitude ocean. We show the global existence and uniqueness of the weak and strong solutions to this model. Moreover, we establish the existence of a finite-dimensional global attractor to this dissipative evolution system. c © 2003 Wiley Periodicals, Inc.

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...