**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**