Global well-posedness for the 3D rotating Boussinesq equations in variable exponent Fourier-Besov spaces

Abstract

<abstract><p>We study the small initial data Cauchy problem for the three-dimensional Boussinesq equations with the Coriolis force in variable exponent Fourier-Besov spaces. Using the Fourier localization argument and Littlewood-Paley decomposition, we obtain the global well-posedness result for small initial data $ (u_0, \theta_0) $ belonging to the critical variable exponent Fourier-Besov spaces $ \mathcal{F}\mathcal{\dot{B}}_{p(\cdot), q}^{2-\frac{3}{p(\cdot)}} $.</p></abstract>