Differential and Integral Equations

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

Lucas C.F. Ferreira and Marcelo F. de Almeida

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356628829

Mathematical Reviews number (MathSciNet)
MR2830704

Zentralblatt MATH identifier
1249.35273

Subjects
Primary: 35Q99: None of the above, but in this section 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 35C06: Self-similar solutions 35B40: Asymptotic behavior of solutions 42B35: Function spaces arising in harmonic analysis

Citation

de Almeida, Marcelo F.; Ferreira, Lucas C.F. On the well posedness and large-time behavior for Boussinesq equations in Morrey spaces. Differential Integral Equations 24 (2011), no. 7/8, 719--742. https://projecteuclid.org/euclid.die/1356628829


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