Global existence and uniqueness for a non linear Boussinesq system in dimension two

Details Global existence and uniqueness for a non linear Boussinesq system in dimension two Global existence and uniqueness for a non linear Boussinesq system in dimension two

2012-03-22

arxiv.org/abs/1203.5045v1

Mathematics

Analysis of PDEs

28 pages; Journal of Mathematics Physics, volume 51, no. 9 (2010)

Scientific paper

We study the global well-posedness of a two-dimensional Boussinesq system
which couples the incompressible Euler equation for the velocity and a
transport equation with fractional diffusion of type $|\DD|^{\alpha}$ for the
temperature. We prove that for $\alpha>1,$ there exists a unique global
solution for initial data with critical regularities.

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