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, Tome 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 : https://doi.org/10.1016/j.anihpc.2014.03.002
Mots clés : Burgers equation, Besov spaces, Large time behavior, Poisson kernel
@article{AIHPC_2015__32_3_687_0,
     author = {Iwabuchi, Tsukasa},
     title = {Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {687--713},
     publisher = {Elsevier},
     volume = {32},
     number = {3},
     year = {2015},
     doi = {10.1016/j.anihpc.2014.03.002},
     zbl = {1320.35073},
     mrnumber = {3353705},
     language = {en},
     url = {www.numdam.org/item/AIHPC_2015__32_3_687_0/}
}
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, Tome 32 (2015) no. 3, pp. 687-713. doi : 10.1016/j.anihpc.2014.03.002. http://www.numdam.org/item/AIHPC_2015__32_3_687_0/

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