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Statistical solutions and degenerate regularity for the non-Newtonian micropolar fluids
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  • Zhao Caidi,
  • Yongkang Zhang,
  • Tomas Caraballo,
  • Grzegorz Lukaszewicz
Zhao Caidi
Wenzhou University

Corresponding Author:zhaocaidi@wzu.edu.cn

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Yongkang Zhang
Wenzhou University
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Tomas Caraballo
Universidad de Sevilla
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Grzegorz Lukaszewicz
University of Warsaw
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Abstract

This paper studies the non-autonomous non-Newtonian micropolar fluids in two-dimensional bounded domains. We first establish that the generated continuous process of the solutions operator possesses a pullback attractor. Then we verify the existence of statistical solutions by constructing the invariant Borel probability measures. Further, we prove that the statistical solutions possess the degenerated regularity of Lusin's type provided that the Grasshof number associated to the external forces is small enough.
03 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
04 Mar 2022Submission Checks Completed
04 Mar 2022Assigned to Editor
25 Mar 2022Reviewer(s) Assigned
23 Nov 2022Editorial Decision: Revise Minor
18 Dec 20221st Revision Received
19 Dec 2022Submission Checks Completed
19 Dec 2022Assigned to Editor
19 Dec 2022Review(s) Completed, Editorial Evaluation Pending
19 Dec 2022Reviewer(s) Assigned
20 Dec 2022Editorial Decision: Accept