Global Mild Solutions to the 3D Boussinesq–Coriolis System With Caputo Time-Fractional Derivatives in Besov–Morrey Spaces

In this article, we investigate the global well-posedness of a three-dimensional incompressible viscous fluid system under the influence of both rotational forces and anomalous diffusion. Specifically, we study a time-fractional Boussinesq– Coriolis model with Caputo derivatives of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> , capturing the combined effects of the Coriolis force and fractional diffusion in geophysical flows. Working within the framework of homogeneous Besov–Morrey spaces, we establish global-in-time existence and uniqueness of mild solutions for small initial data. Our analysis relies on refined semigroup estimates associated with the Stokes–Coriolis operator, together with properties of the Mittag–Leffler and Mainardi functions. This extends prior results in classical and fractional Boussinesq or Navier–Stokes systems by incorporating both time-fractional dynamics and rotation.