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 - <p style="text-align: justify;">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&nbsp; $ \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.</p>