Regularity criterion for the 3D magneto-micropolar fluid flows in terms of pressure.
Simiao Yan and Xiaoli Chen
School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China
Received on February 6, 2022, revised version on December 3, 2022
Accepted on January 27, 2023
Communicated by Stanislas Ouaro
| Abstract. In this note, we obtain a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of pressure. More precisely, we prove that if π ∈ L2/ (2−r) (0, T;L3/r (R3)) with 0 < r ≤ 1, then the local strong solution (u, b, ω) to the magneto-micropolar fluid flows can be extended beyond time t = T. Meanwhile we also show that provided that π ∈ Lp(0, T; F'0 q, 10q/ (5q+6) (R3)) with 2/p + 3/q < 7/4, 12/5 < q ≤ ∞ or ∇π ∈ Lp(0, T; F'0q, 8q/(12-3q) (R3)) with 2/p + 3/q = 11/4, 12/11 < q < 4, the weak solution (u, b, ω) to the magneto-micropolar fluid flows can also be extended smoothly beyond t = T. | |
| Keywords: | Magneto-micropolar equations; blow up criterion; Weak solution; Triebel-Lizorkin spaces; Pressure; Regularity criterion. |
| 2010 Mathematics Subject Classification: 35Q35; 76D03. | |