Beale-Kato-Majda type condition for Burgers equation

Details Beale-Kato-Majda type condition for Burgers equation Beale-Kato-Majda type condition for Burgers equation

2008-02-19

arxiv.org/abs/0802.2733v2

Mathematics

Analysis of PDEs

21 pages, accepted to "Journal of mathematical analysis and applications"

Scientific paper

We consider a multidimensional Burgers equation on the torus $\mathbb{T}^d$ and the whole space $\Rd$. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of $\Rd$ we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove these results we use the probabilistic arguments which seem to be new.

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