# Existence and stability of non linear almost compressible convective flows for Bénard's problem - A. De Martino (Università di Ferrara)

## Dettagli dell'evento

### Quando

29/03/2019
dalle 11:30 alle 12:30

### Dove

Aula B1, Palazzo Manfredini

M. Miranda

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Abstract

We study the non linear almost compressible Oberbeck-Boussinesq system which
Is characterized by an extra buoyancy term where the density depends on the pressure.
The 2D Bernard’s problem depends on a new dimensionless parameter $\hat{\beta}$, which
Is proportional to the positive compressibility factor $\beta$. The existence and
The stability of the perturbation to the basic solution is shown. The proof is based
On the direct sum of two invariant orthogonal subspaces related to the geometry.
The non linear stability of the rest state relies on $\Ra$ sufficiently
small.