**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. **