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Lower bounds of decay rates for the MHD micropolar equations

Author

Listed:
  • Cruz, Felipe W.
  • Freitas, Lorena B.S.

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.

Suggested Citation

  • Cruz, Felipe W. & Freitas, Lorena B.S., 2024. "Lower bounds of decay rates for the MHD micropolar equations," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011718
    DOI: 10.1016/j.chaos.2024.115619
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