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Statistical solution and partial degenerate regularity for the 2D non-autonomous magneto-micropolar fluids

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Abstract

In this article, the authors investigate the non-autonomous magneto-micropolar fluids in a two-dimensional bounded domain. They first prove the existence of a pullback attractor for the associated process. Then, they construct a family of invariant Borel probability measures supported on the pullback attractor and prove that this family of probability measures is indeed a statistical solution for the magneto-micropolar fluids. Further, they establish that if some form of the Grashof number is small enough, then the pullback attractor degenerates to a single bounded complete trajectory, which implies the partial degenerate regularity of the statistical solution in the sense that it is supported on a set in which the weak solutions are in fact partially strong solutions.

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Authors and Affiliations

  1. Department of Mathematics, Wenzhou University, Wenzhou, 325035, Zhejiang Province, People’s Republic of China

    Caidi Zhao & Yanjiao Li

  2. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Grzegorz Łukaszewicz

Authors
  1. Caidi Zhao
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  2. Yanjiao Li
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  3. Grzegorz Łukaszewicz
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Correspondence to Caidi Zhao.

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Supported by NSF of China with Nos. 11971356, 11271290 and by NSF of Zhejiang Province with No. LY17A010011. Also by National Science Center (NCN) of Poland under Project No. DEC-2017/25/B/ST1/00302.

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Zhao, C., Li, Y. & Łukaszewicz, G. Statistical solution and partial degenerate regularity for the 2D non-autonomous magneto-micropolar fluids. Z. Angew. Math. Phys. 71, 141 (2020). https://doi.org/10.1007/s00033-020-01368-8

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  • DOI: https://doi.org/10.1007/s00033-020-01368-8

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