Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics

Details Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics

2012-01-30

arxiv.org/abs/1201.6326v1

Mathematics

Analysis of PDEs

13

Scientific paper

We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the $N$-dimensional case. In the second part of the paper, our method is adapted to handle the axisymmetric incompressible Euler equations with swirl.

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