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 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 to show that the solution behaves like the 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}, mrnumber = {3353705}, zbl = {1320.35073}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2014.03.002/} }
TY - JOUR AU - Iwabuchi, Tsukasa TI - Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 687 EP - 713 VL - 32 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2014.03.002/ DO - 10.1016/j.anihpc.2014.03.002 LA - en ID - AIHPC_2015__32_3_687_0 ER -
%0 Journal Article %A Iwabuchi, Tsukasa %T Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 687-713 %V 32 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2014.03.002/ %R 10.1016/j.anihpc.2014.03.002 %G en %F 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, 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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