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On the large time decay of asymmetric flows in homogeneous Sobolev spaces

2018; Elsevier BV; Volume: 471; Issue: 1-2 Linguagem: Inglês

10.1016/j.jmaa.2018.10.065

ISSN

1096-0813

Autores

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

Tópico(s)

Fluid Dynamics and Turbulent Flows

Resumo

In this paper, the large time decay of the micropolar fluid equations on H˙s(Rn) (where n=2,3 and s≥0) are studied. We show, for each s≥0, that ts/2‖(u,w)(⋅,t)‖H˙s(Rn)→0 as t→∞ for Leray global solutions with 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(ts+12). Some related results are also included.

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