On product estimates in Besov-Morrey spaces and stationary solutions for the Hall-MHD and Navier-Stokes systems

Abstract

In this paper, we investigate the well-posedness of the three-dimensional stationary incompressible resistive-viscous Hall magnetohydrodynamic (Hall-MHD) system within the framework of scale-invariant Besov-Morrey spaces. A key component of our analysis is the derivation of product estimates in these spaces, which are instrumental in handling the system's nonlinear terms. As an application, we also establish a well-posedness result for the stationary Navier-Stokes equations in this setting, thereby broadening the admissible classes of external forces and solutions.