PhD
THESIS DEFENSE
INSTITUTO DE CIENCIAS MATEMÁTICAS

PHD STUDENT: Daniel Lear (ICMAT)

ADVISORS: Diego Córdoba (ICMAT) and Ángel Castro (ICMAT)

DATE: Friday, 29 March 2019 - 12:00
VENUE: Aula Naranja, 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. 1st: The inviscid incompressible
porous media equation. 2nd: The inviscid and non-diffusive Boussinesq system
with a velocity damping term.
STABILITY NEAR HYDROSTATIC
EQUILIBRIUM IN FLUID MECHANICS