Year: 2026
Type: preprint
Abstract: In this paper, we consider the Cauchy problem for the incompressible magnetohydrodynamic equations with the Coriolis force in the three-dimensional whole space. For large initial data, it is known that the Cauchy problem admits a unique global solution in critical Sobolev space $\dot{H}^{1/2}(\mathbb{R}^3)$ provided that the speed of rotation is fast enough. By using delicate dispersive estimates, we show refined decay estimates of the velocity field and magnetic field. These decay rates significantly improve the ones obtained by Kim [\emph{J. Differential Equations.}, 2022] in the subcritical Sobolev framework $H^s(\mathbb{R}^3)$ with $1/2
Source: arXiv (Cornell University)
Authors: Fujii, Mikihiro, Li, Yang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3402004506, G5332886115
OpenAlex ID: W7204901511