### AIMS Mathematics

2019, Issue 3: 910-927. doi: 10.3934/math.2019.3.910
Research article

# The zero-energy limit and quasi-neutral limit of scaled Euler-Maxwell system and its corresponding limiting models

• Received: 08 May 2019 Accepted: 10 July 2019 Published: 26 July 2019
• MSC : Primary: 34E05, 35Q35, 35L60; Secondary: 35Q61

• In this paper, we apply a new scaling for Euler-Maxwell system. As a result, zero-energy limit is introduced, combining it with quasi-neutral limit, we obtain a complete system of the limiting models for Euler-Maxwell system. The asymptotic analysis and a weighted energy method are used to rigorously justify the zero-energy limit for e-MHD, which is the limiting model of Euler-Maxwell system as the Debye length tends to zero. For other limits, we provide a formal derivation and obtain an approximate asymptotic expansion.

Citation: Tariq Mahmood. The zero-energy limit and quasi-neutral limit of scaled Euler-Maxwell system and its corresponding limiting models[J]. AIMS Mathematics, 2019, 4(3): 910-927. doi: 10.3934/math.2019.3.910

### Related Papers:

• In this paper, we apply a new scaling for Euler-Maxwell system. As a result, zero-energy limit is introduced, combining it with quasi-neutral limit, we obtain a complete system of the limiting models for Euler-Maxwell system. The asymptotic analysis and a weighted energy method are used to rigorously justify the zero-energy limit for e-MHD, which is the limiting model of Euler-Maxwell system as the Debye length tends to zero. For other limits, we provide a formal derivation and obtain an approximate asymptotic expansion.

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