Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 71, Issue 4, Pages -Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-020-01368-8
Keywords
Statistical solution; Invariant Borel probability measure; Degenerate regularity; Magneto-micropolar fluid; Pullback attractor
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Funding
- NSF of China [11971356, 11271290]
- NSF of Zhejiang Province [LY17A010011]
- National Science Center (NCN) of Poland [DEC-2017/25/B/ST1/00302]
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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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