Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 3, pp. 687-713.

We consider the Cauchy problem for the critical Burgers equation. The existence and the uniqueness of global solutions for small initial data are studied in the Besov space B ˙ ,1 0 ( n ) and it is shown that the global solutions are bounded in time. We also study the large time behavior of the solutions with the initial data u 0 L 1 ( n )B ˙ ,1 0 ( n ) to show that the solution behaves like the Poisson kernel.

DOI: 10.1016/j.anihpc.2014.03.002
Keywords: Burgers equation, Besov spaces, Large time behavior, Poisson kernel
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Iwabuchi, Tsukasa. Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 3, pp. 687-713. doi : 10.1016/j.anihpc.2014.03.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.03.002/

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