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 ${\stackrel{˙}{B}}_{\infty ,1}^{0}\left({ℝ}^{n}\right)$ 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 ${u}_{0}\in {L}^{1}\left({ℝ}^{n}\right)\cap {\stackrel{˙}{B}}_{\infty ,1}^{0}\left({ℝ}^{n}\right)$ 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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