TY - JOUR T1 - Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces AU - Azanzal , Achraf AU - Allalou , Chakir AU - Melliani , Said AU - Abbassi , Adil JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 21 PY - 2022 DA - 2022/12 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/21290.html KW - 2D quasi-geostrophic equation KW - subcritical dissipation KW - Littlewood-Paley theory KW - global well-posedness KW - long time behavior of the solution KW - Fourier-Besov-Morrey spaces. AB -

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.