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.
Qunyi BIE
,
Hao CHEN
. ON ALMOST AXISYMMETRIC INCOMPRESSIBLE MAGNETOHYDRODYNAMICS IN THREE DIMENSIONS[J]. Acta mathematica scientia, Series B, 2025
, 45(2)
: 446
-472
.
DOI: 10.1007/s10473-025-0210-y
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