This work proves the convergence in L¹(ℝ²) towards an Oseen vortex-like solution to the dissipative quasi-geostrophic equations for several sets of initial data with suitable decay at infinity. The relative entropy method applies in a direct way for solving this question in the case of signed initial data and the difficulty lies in showing the existence of unique global solutions for the class of initial data for which all properties needed in the entropy approach are met. However, the estimates obtained for the constructed global solutions in L¹ ∩ L² show the asymptotic simplification of the solutions even for unsigned initial data emphasizing the character of this equation to behave linearly for large times.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-5,
author = {Jos\'e A. Carrillo and Lucas C. F. Ferreira},
title = {Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {95-115},
zbl = {1121.35109},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-5}
}
José A. Carrillo; Lucas C. F. Ferreira. Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations. Banach Center Publications, Tome 72 (2006) pp. 95-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-5/