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

Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 446-472.doi: 10.1007/s10473-025-0210-y

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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).

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

CLC Number:

35Q35

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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