ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS

ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS

ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS

ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS

ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS

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doi:10.1007/s10473-025-0210-y

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (2): 446-472.doi: 10.1007/s10473-025-0210-y

Qunyi Bie¹, Hao Chen^2,*

1. College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China;
2. College of Science, China Three Gorges University, Yichang 443002, China

收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2025-03-25 发布日期:2025-05-08

Qunyi Bie¹, Hao Chen^2,*

1. College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China;
2. College of Science, China Three Gorges University, Yichang 443002, China

Received:2022-11-20 Revised:2023-01-08 Online:2025-03-25 Published:2025-05-08
Contact: *Hao Chen, E-mail: chenhao215@outlook.com
About author:Qunyi Bie, E-mail: qybie@126.com
Supported by:
The first author's work was supported by the National Natural Science Foundation of China (11871305).

摘要： In this paper, we study the Cauchy problem of three-dimensional incompressible magnetohydrodynamics with almost symmetrical initial values in the cylindrical coordinates. Here the almost axisymmetric means that $(\partial_\theta u^r_0,\partial_\theta u^\theta_0,\partial_\theta u^z_0)$ is small. With additional smallness assumption on $(u^\theta_0,b^\theta_0)$ , we prove the global existence of a unique strong solution $(\boldsymbol{u},\boldsymbol{b})$ , which keeps close to some axisymmetric vector fields. Moreover, we give the initial data with some special symmetric structures that will persist for all time.

关键词: magnetohydrodynamics, almost symmetrical, cylindrical coordinates

Abstract: In this paper, we study the Cauchy problem of three-dimensional incompressible magnetohydrodynamics with almost symmetrical initial values in the cylindrical coordinates. Here the almost axisymmetric means that $(\partial_\theta u^r_0,\partial_\theta u^\theta_0,\partial_\theta u^z_0)$ is small. With additional smallness assumption on $(u^\theta_0,b^\theta_0)$ , we prove the global existence of a unique strong solution $(\boldsymbol{u},\boldsymbol{b})$ , which keeps close to some axisymmetric vector fields. Moreover, we give the initial data with some special symmetric structures that will persist for all time.

Key words: magnetohydrodynamics, almost symmetrical, cylindrical coordinates

中图分类号:

35Q35

Qunyi Bie, Hao Chen. ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS[J]. 数学物理学报(英文版), 2025, 45(2): 446-472.

Qunyi Bie, Hao Chen. ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS[J]. Acta mathematica scientia,Series B, 2025, 45(2): 446-472.

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