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

Voir la notice de l'article provenant de la source Numdam

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
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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, Tome 32 (2015) no. 3, pp. 687-713. doi: 10.1016/j.anihpc.2014.03.002

Cité par Sources :