Large time behavior of the Euler-Poisson system coupled to a magnetic field

Yingying Chen; Lan Huang; Jianwei Yang; Yingying Chen; Lan Huang; Jianwei Yang

doi:10.3934/math.2023580

AIMS Mathematics

2023, Volume 8, Issue 5: 11460-11479. doi: 10.3934/math.2023580

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Research article

Large time behavior of the Euler-Poisson system coupled to a magnetic field

School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, Henan Province, China

Received: 27 January 2023 Revised: 03 March 2023 Accepted: 07 March 2023 Published: 14 March 2023
MSC : 35B35, 35B40, 35M10

In this paper, the large time behavior of globally smooth solutions of the Cauchy problem for the three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field is studied. We prove that the smooth solutions (near a given constant equilibrium state) of the problem converge asymptotically to a stationary solution exponentially fast as $ t $ goes to $ \infty $.
- stability,
- asymptotic behavior of solutions,
- Euler-Poisson system,
- magnetic field
Citation: Yingying Chen, Lan Huang, Jianwei Yang. Large time behavior of the Euler-Poisson system coupled to a magnetic field[J]. AIMS Mathematics, 2023, 8(5): 11460-11479. doi: 10.3934/math.2023580

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Abstract

In this paper, the large time behavior of globally smooth solutions of the Cauchy problem for the three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field is studied. We prove that the smooth solutions (near a given constant equilibrium state) of the problem converge asymptotically to a stationary solution exponentially fast as $ t $ goes to $ \infty $.

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