Lower bounds of decay rates for the MHD micropolar equations

Felipe W. Cruz and Lorena B.S. Freitas

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: We derive lower bounds for the decay rates of solutions to the 3D equations describing the motion of a micropolar fluid under the influence of a magnetic field. To accomplish this, we establish a lower bound for the decay of the solution (u¯,w¯,b¯) of the linearized system, as well as an upper bound for the difference (u−u¯,w−w¯,b−b¯), where (u,w,b) represents the solution of the full nonlinear system. More specifically, for a certain class of initial data, we prove that ‖u(⋅,t)‖L2(R3)2+‖w(⋅,t)‖L2(R3)2+‖b(⋅,t)‖L2(R3)2≥C(t+1)−32, for all t≥0.

Keywords: Decay rates; Large time behavior; Lower bounds; Magneto-micropolar fluids; Spectral analysis; Temporal decay estimates (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011718

DOI: 10.1016/j.chaos.2024.115619

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