Time Decay Estimates of Solutions to the Magnetic Bénard System in a Half-Space

This paper aims to derive the time decay estimates for both weak and strong solutions to the incompressible magnetic Bénard system in a half-space. To address the technical challenges posed by the boundary effects in unbounded domains, we primarily employ L q − L r estimates, together with properties of the Stokes operator and a suitable decomposition of the nonlinear terms. We establish the L 2 -estimates of weak solutions and obtain the L q ( 1 ≤ q ≤ ∞ ) -estimates of strong solutions and their first three derivatives. In addition, if the given initial data belongs to a suitable weighted space, more optimal decay effects are established.