Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces

Details Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces

Publishing date

2008-06-25

URL

arxiv.org/abs/0806.4084v1

Science

Mathematics

Field

Analysis of PDEs

Additional info

24 pages. Physica D, in press

Type

Scientific paper

Digital Object Identifier

10.1016/j.physd.2008.03.034

Abstract

This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension $N\geq3.$ First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is at the scaling of the equations. Second, we get a uniqueness result in Besov spaces with {\it negative} indices of regularity (despite the fact that there is no smoothing effect on the temperature). The proof relies on a priori estimates with loss of regularity for the nonstationary Stokes system with convection. As a corollary, we obtain a global existence and uniqueness result for small data in Lorentz spaces.

Affiliated with

Also associated with

No associations

Rating

Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162674