SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

doi:10.1007/s10473-025-0317-1

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 1063-1077.doi: 10.1007/s10473-025-0317-1

SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

Zhen QIU, Guangwu WANG^†

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

收稿日期:2023-11-14 修回日期:2024-04-11 出版日期:2025-05-25 发布日期:2025-09-30

SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

Zhen QIU, Guangwu WANG^†

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received:2023-11-14 Revised:2024-04-11 Online:2025-05-25 Published:2025-09-30
Contact: ^†Guangwu WANG, E-mail: yunxianwgw@163.com
About author:Zhen QIU, E-mail: qiuzhen97@foxmail.com
Supported by:
The Postgraduate Innovation Project of Guangzhou University (Grant No. JCCX2024-13). National Natural Science Foundation of China (Grant No. 11801107).

摘要/Abstract

摘要： In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500-2516].

关键词: Navier-Stokes-Landau-Lifshitz system, Serrin-type blow-up criterion, Besov space with the negative index

Abstract: In this paper, we consider the two-dimensional incompressible Navier-Stokes-Landau-Lifshitz system. The first result is the classical Serrin-type blow-up criterion for Navier-Stokes-Landau-Lifshitz system whose index is the same as Navier-Stokes equation. More generally, we establish the blow-up criterion in the homogenous Besov space with the negative index whose form is analogue to Serrin-type. As a result, the blow-up criterion in BMO space with respect to spatial variable is also attained. These results can be regarded as the extension of the recent work [Math. Methods Appl. Sci. 46, (2023), 2500-2516].

Key words: Navier-Stokes-Landau-Lifshitz system, Serrin-type blow-up criterion, Besov space with the negative index

中图分类号:

35B44

Zhen QIU, Guangwu WANG. SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM[J]. 数学物理学报(英文版), 2025, 45(3): 1063-1077.

Zhen QIU, Guangwu WANG. SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM[J]. Acta mathematica scientia,Series B, 2025, 45(3): 1063-1077.

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SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

SERRIN-TYPE BLOW-UP CRITERIA FOR 2D INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ SYSTEM

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