Beale-kato-majda Type Condition for Burgers Equation
نویسندگان
چکیده
We consider a multidimensional Burgers equation on the torus T and the whole space R . 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 R 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. In this paper we are concerned with the following multidimensional Burgers equation: ∂ui ∂t + n
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