Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 3
138
Views
2
CrossRef citations to date
0
Altmetric
Articles

Regularizing rate estimates for the 3-D incompressible micropolar fluid system in critical Besov spaces

&
Pages 428-446 | Received 17 Jul 2017, Accepted 10 Jul 2018, Published online: 31 Jul 2018
 

ABSTRACT

In this paper, we are concerned with regularizing rates of the higher order derivatives of solutions for the initial value problem of a three-dimensional incompressible micropolar fluid system with initial data (u0,ω0)a˙Bp,1+3/p(R3) for 1p<6. More precisely, we prove that there exist two positive constants K1 and K2 such that for any βN03, the B˙q,s-norm of β-order derivatives of solutions obeys the following regularizing rates: (xβu(,t),xβω(,t))B˙q,sK1(K2|β|)|β|t|β|/2(1/2)(s+13/q) for some suitable choices of s and q. These estimates particularly imply the spatial analyticity and the temporal decay of global solutions.

COMMUNICATED BY:

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgments

The authors sincerely acknowledge their gratefulness to the referees for the valuable comments and suggestions, and to Professor Shangbin Cui for his warm guidance.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

W. Zhu is partially supported by the National Natural Science Foundation of China (11571381). J. Zhao is partially supported by the National Natural Science Foundation of China (11501453) and the Natural Science Foundation of Shaanxi Province (2018JM1004, 2017JM1016).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.