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Time asymptotic profiles to the magneto-micropolar system

2019; Taylor & Francis; Volume: 99; Issue: 15 Linguagem: Inglês

10.1080/00036811.2019.1578347

1563-504X

Cilon Perusato, Wilberclay G. Melo, Robert Guterres, Juliana R. Nunes,

Stability and Controllability of Differential Equations

This work examines some decay properties of solutions to the Cauchy problem for the magneto-micropolar fluid equations on H˙s(Rn) (where n=2,3 and s≥ 0 real). We show, for each s≥ 0, that ts/2∥(u,w,b)(⋅,t)∥H˙s(Rn)→0 as t→∞ for Leray global solutions with an arbitrary initial data in L2(Rn). When the vortex viscosity is present, we obtain a (faster) decay for the micro-rotational field: ∥w(⋅,t)∥H˙s(Rn)=o(t(s+1)/2). Some related results are also included.