Beale-Kato-Majda type condition for Burgers equation

الأصل · EN

We consider a multidimensional Burgers equation on the torus Tᵈ and the whole space. 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 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.