Existence of a global weak solution for a 2D viscous bi-layer Shallow Water model

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...

Global Weak Solutions for a Shallow Water Equation

where α, γ, ω are given real constants. Equation (1) was first introduced as a model describing propagation of unidirectional gravitational waves in a shallow water approximation over a flat bottom, with u representing the fluid velocity [DGH01]. For α = 0 and for α = 1, γ = 0 we obtain the Korteweg–de Vries and the Camassa–Holm [CH93, J02] equations, respectively. Both of them describe unidire...

Strong solutions for a 1D viscous bilayer Shallow Water model

In this paper, we consider a viscous bilayer shallow water model in one space dimension that represents two superposed immiscible fluids. For this model, we prove the existence of strong solutions in a periodic domain. The initial heights are required to be bounded above and below away from zero and we get the same bounds for every time. Our analysis is based on the construction of approximate ...

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

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