arXiv subjects

Rafael P. da Silva

Publications and source records attributed to Rafael P. da Silva.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2024

On the well-posedness of the Hall-MHD system in a critical setting of Besov-Morrey type

In this paper, we address the 3D incompressible Hall-magnetohydrodynamic system (Hall-MHD). Our objective is to provide local and global well-posedness results for initial velocity $u_{0}$, magnetic field $B_{0}$ and the current $J_{0}:=\nabla\times B_{0}$ in a new critical framework, namely critical Besov-Morrey spaces. These spaces combine typical characteristics from both Besov and Morrey spaces allowing a broader framework that encompasses the regularity properties inherent in Besov spaces with the Morrey space structure. Compared to previous works in Sobolev and Besov spaces, our approach accommodates a broader class of initial data, ensuring the construction of a unique solution over time.

math.AP↗