Regularizing rate estimates for the 3-D incompressible micropolar fluid system in critical Besov spaces. Issue 3 (17th February 2020)

• Record Type: Journal Article
• Authors: Zhu, Weipeng; Zhao, Jihong
• Is Part Of: Applicable analysis. Volume 99:Issue 3(2020)
• Page Start: 428
• Page End: 446
• Publication Date: 2020-02-17
• Subjects: Bo Zhang; Micropolar fluid system -- regularizing rate -- spatial analyticity -- temporal decay -- Besov spaces; 35B65 -- 35K45 -- 35Q35 -- 76D03; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1501029
• Languages: English
• ISSNs: 0003-6811

Abstract

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 ( u 0, ω 0 ) ∈ a ˙ B p, ∞ − 1 + 3 / p ( R 3 ) for 1 ≤ p < 6 . More precisely, we prove that there exist two positive constants K 1 and K 2 such that for any β ∈ N 0 3, the B ˙ q, ∞ s -norm of β -order derivatives of solutions obeys the following regularizing rates: ∥ ( ∂ x β u ( ⋅, t ), ∂ x β ω ( ⋅, t ) ) ∥ B ˙ q, ∞ s ≤ K 1 ( K 2 | β | ) | β | t − | β | / 2 − ( 1 / 2 ) ( s + 1 − 3 / q ) for some suitable choices of s and q . These estimates particularly imply the spatial analyticity and the temporal decay of global solutions.