@article{91c17d2ecb484843b469949f17b15342,

title = "Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation",

abstract = "This paper is concerned with the Cauchy problem of the Burgers equation with the critical dissipation. The well-posedness and analyticity in both of the space and the time variables are studied based on the frequency decomposition method. The large time behavior is revealed for any large initial data. As a result, it is shown that any smooth and integrable solution is analytic in space and time as long as time is positive and behaves like the Poisson kernel as time tends to infinity. The corresponding results are also obtained for the quasi-geostrophic equation.",

keywords = "Analyticity in space and time, Burgers equation, Critical dissipation, Large data, Large time behavior, Quasi-geostrophic equation",

author = "Tsukasa Iwabuchi",

note = "Funding Information: The author would like to thank the referees for their thoughtful comments. The author was supported by the Grant-in-Aid for Young Scientists (A) (No. 17H04824 ) from JSPS and by Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers from JSPS . Publisher Copyright: {\textcopyright} 2020 The Author",

year = "2020",

month = jul,

day = "1",

doi = "10.1016/j.anihpc.2020.02.003",

language = "English",

volume = "37",

pages = "855--876",

journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",

issn = "0294-1449",

publisher = "Elsevier Masson SAS",

number = "4",

}