@Article{JPDE-36-1, author = {Azanzal , AchrafAllalou , ChakirMelliani , Said and Abbassi , Adil}, title = {Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {36}, number = {1}, pages = {1--21}, abstract = {

In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists $v$ a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces  $ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}$. Moreover, we show the asymptotic behavior of the global solution $v$. i.e., $\|v(t)\|_{ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}}$ decays to zero as time goes to infinity.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/21290.html} }