Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow

被引：16
|
作者：
Zeng, Lan [1 ]
Zhang, Zhifei [1 ]
Zi, Ruizhao [2 ,3 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 40079, Peoples R China
[3] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 40079, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2021年 / 280卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Patlak-Keller-Segel equation; Navier-Stokes equation; Couette flow; Enhanced dissipation;
D O I：
10.1016/j.jfa.2021.108967
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the two dimensional Patlak-Keller-Segel-Navier-Stokes system near the Couette flow (Ay, 0) in T x R. It is shown that if A is large enough, the solution to the system stays globally regular. Both the parabolic-parabolic case and the parabolic-elliptic case are investigated. In particular, for the parabolic-parabolic case, an extra smallness assumption on the initial chemical gradient parallel to(del c(in))not equal parallel to(L2) is needed to control the mixing destabilizing effect. (C) 2021 Elsevier Inc. All rights reserved.
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