Quasineutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data

Min Li; Xueke Pu; Shu Wang; Min Li; Xueke Pu; Shu Wang

doi:10.3934/era.2020046

Electronic Research Archive

2020, Volume 28, Issue 2: 879-895. doi: 10.3934/era.2020046

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Quasineutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data

Min Li ^{1
,},
Xueke Pu ^{2
,
,},
Shu Wang ^{3
,}

1.
Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
3.
College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Received: 01 April 2020 Revised: 01 April 2020
Primary: 35L60, 35B40; Secondary: 35C20

In this paper, we study the quasi-neutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data. Precisely, we proved the solution of the three-dimensional compressible two-fluid Euler–Maxwell equations converges locally in time to that of the compressible Euler equation as $ \varepsilon $ tends to zero. This proof is based on the formal asymptotic expansions, the iteration techniques, the vector analysis formulas and the Sobolev energy estimates.
- Two-fluid Euler–Maxwell equations,
- quasi-neutral limit,
- uniform energy estimates,
- singular perturbation methods,
- formal asymptotic expansions
Citation: Min Li, Xueke Pu, Shu Wang. Quasineutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data[J]. Electronic Research Archive, 2020, 28(2): 879-895. doi: 10.3934/era.2020046

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Abstract

In this paper, we study the quasi-neutral limit for the compressible two-fluid Euler–Maxwell equations for well-prepared initial data. Precisely, we proved the solution of the three-dimensional compressible two-fluid Euler–Maxwell equations converges locally in time to that of the compressible Euler equation as $ \varepsilon $ tends to zero. This proof is based on the formal asymptotic expansions, the iteration techniques, the vector analysis formulas and the Sobolev energy estimates.

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