Daniel Lear Claveras : Stability Near Hydrostatic Equilibrium in Fluid Mechanics

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

Sept. 30, 2019, 4 p.m.

In

636 SEO

Abstract

A fluid is said to be in hydrostatic equilibrium when it is at rest. Then the forces acting on it must balance it. A natural question therefore arises: What happens if our initial data is close to an hydrostatic equilibrium solution? The field of hydrodynamic stability has a long history starting in the 19th century. For us, the basic problem is to consider a perturbation of the hydrostatic equilibrium, in which case the fluid must start to move, and to study the long-time behavior of the solution. In this talk, we study the stability of the hydrostatic equilibrium in two different problems. 1st: The inviscid incompressible porous media equation. 2nd: The inviscid and non-diffusive Boussinesq system with a velocity damping term.