Prelectura de tesis

TITLE: Stability Near Hydrostatic Equilibrium in Fluid Mechanics

PHD STUDENT: Daniel Lear

PHD THESIS ADVISORS: Diego Córdoba and Ángel Castro

DATE: Thursday 20 December 2018 - 12:00

VENUE: Aula 520, Módulo 17, Departamento de Matemáticas, UAM

ORGANISER: UAM - ICMAT

ABSTRACT: A fluid is said to be in hydrostatic
equilibrium when it is at rest. If the fluid 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 hydrodinamic 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
particular, we focus on laminar equilibria, even for these
simple configurations surprisingly little is understood about the
near equilibrium dynamics.

In this talk, we study the stability of the hidrostatic equilibrium in
two different problems inside the field of fluid mechanics.
1º The inviscid incompressible porous media equation.
2º The inviscid and non-diffusive Boussinesq system with a velocity
damping term.