## Differential and Integral Equations

### On the well posedness and large-time behavior for Boussinesq equations in Morrey spaces

#### Abstract

In this paper we are concerned with Boussinesq equations which model heat transport by natural convection inside a viscous incompressible fluid in $\mathbb{R} ^{n}$. We prove the well posedness of mild solutions and existence of self-similar ones in the framework of Morrey spaces. Our results allow us to consider singular and unbounded gravitational fields. We also study the long-time behavior of solutions and obtain existence of a basin of attraction for each self-similar solution. Moreover, conditions on initial data for solutions to vanish at infinity are given.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 7/8 (2011), 719-742.

Dates
First available in Project Euclid: 27 December 2012