Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

Homogeneous Plane-wave Spacetimes and their Stability

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4 + 1) dimensions, and find there are two cases to consider; what we call nonexceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In...

Existence of solutions for compressible fluid models of Korteweg type

This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) in [15, 25], which can be used as a phase transition model. We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and w...

Long Time Stability for Solutions of a Β-plane Equation

We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the 2d incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of no...

Studying the Effect of Horizontal Drains on Stability of Heterogeneous and Homogeneous Earth Dams during Rapid Drawdown Condition

One of the main concerns to design earth dam is the stability of the upstream slope of the earth dam in phase of rapid drawdown. Confined pore water pressure reduces the effective stress in this mode, so possibility of the instability and slippage will be increased. The main goal of this research is to investigate changes in the pore water pressure by using horizontal drains in upstream slope o...