Regularity criterion for 3D generalized Newtonian fluids in BMO

被引：2
|
作者：
Sin, Cholmin [1 ]
Baranovskii, Evgenii S. [2 ]
机构：
[1] State Acad Sci, Inst Math, Pyongyang, North Korea
[2] Voronezh State Univ, Dept Appl Math Informat & Mech, Voronezh, Russia
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 377卷
关键词：
Generalized Navier-Stokes equations; Non-Newtonian fluids; Shear-dependent viscosity; Regularity criterion; Gagliardo-Nirenberg inequality; BMO; NAVIER-STOKES EQUATIONS; SHEAR THINNING FLUIDS; WEAK SOLUTIONS; ONE-COMPONENT; VELOCITY; EXISTENCE;
D O I：
10.1016/j.jde.2023.10.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that a weak solution of the Cauchy problem for 3D unsteady flows of a generalized Newtonian fluid becomes a strong solution for 5/3 < p < 11/5 provided that the velocity field belongs to the critical space L (2/ p-1) (0, T; BMO(R-3)). The main key is to apply variants of Gagliardo-Nirenberg's inequality including a BMO-norm. In particular, when 2 < p < 11/5 , we derive and use a nonlinear variant p-2 of Gagliardo-Nirenberg's inequality including IIuII(BMO) and II|Du| (p-2/2) del( 2)uII2.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：859 / 872
页数：14
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