On the Liouville Theorems for 3D Stationary Magnetohydrodynamic Equations

TIAN Qin; XIANG Changlin; BIE Qunyi

doi:10.21656/1000-0887.430375

Volume 44 Issue 10

Oct. 2023

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TIAN Qin, XIANG Changlin, BIE Qunyi. On the Liouville Theorems for 3D Stationary Magnetohydrodynamic Equations[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1250-1259. doi: 10.21656/1000-0887.430375

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On the Liouville Theorems for 3D Stationary Magnetohydrodynamic Equations

doi: 10.21656/1000-0887.430375

TIAN Qin^{1, 2
,},
XIANG Changlin^{1, 2
,
,},
BIE Qunyi^{1, 2
,}

1.
College of Science, China Three Gorges University, Yichang, Hubei 443002, P.R. China
2.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P.R. China

Received Date: 2022-11-22
Rev Recd Date: 2023-03-04
Publish Date: 2023-10-31

Abstract

Abstract

The Liouville theorems for 3D stationary magnetohydrodynamic equations were studied. First, a Caccioppoli type inequality was obtained with the energy method, then 3 sufficient conditions for the Liouville theorems were obtained based on the Sobolev embedding theorems, of which 1 sufficient condition indicates that, given a smooth solution to the 3D stationary magnetohydrodynamic equation satisfying( u , b )∈L^p, 3/2 < p < 3, equality u = b ≡ 0 will be tenable. This work extends the lower bound of the integrable index in the Lebesgue space from 2 to 3/2 without the finite Dirichlet integral condition, which improves and generalizes some conclusions about the Liouville theorems for stationary magnetohydrodynamic equations.
- magnetohydrodynamic equations,
- Liouville theorems,
- Caccioppoli type inequality

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References(17)

References

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