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Abstract: 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 aunique global solution in Lebesgue spaces. For a torus we also provideestimates on the large time behaviour of solutions. In the case of $\Rd$ weestablish the existence of a unique global solution if a Beale-Kato-Majda typecondition is satisfied. To prove these results we use the probabilisticarguments which seem to be new.



Autor: Ben Goldys, Misha Neklyudov

Fuente: https://arxiv.org/







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