The non-relativistic limit of Euler–Maxwell equations for two-fluid plasma

Yang, Jianwei; Wang, Shu

doi:10.1016/j.na.2009.09.024

Cited by 20 publications

(11 citation statements)

References 17 publications

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“…Hence the singular limit theory for symmetrizable hyperbolic systems developed by Klainerman and Majda 18 or extended further by Schochet 19 cannot be applied here to obtain the uniformly a priori estimates of the solution V τ with respect to τ . This assumption is obviously not satisfied by our present system (8). Usually it is difficult to establish uniformly a priori estimates on the error F τ of the electric field with respect to due to the singular structure of the matrix D τ 0 .…”

Section: Derivation Of Error Equations and Local Existencementioning

confidence: 91%

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The combined relaxation and non-relativistic approximation of the drift-diffusion model

Yang

Yang²

2012

ScienceAsia

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Section: Derivation Of Error Equations and Local Existencementioning

confidence: 91%

“…In this section, we give a construction of the approximation (n τ , u τ , E τ , B τ ) in the convergence assumption for the Euler-Maxwell system (8). Let (N , E) solve the IVP of the unipolar drift-diffusion model (10).…”

Section: Formal Approximationsmentioning

confidence: 99%

The combined relaxation and non-relativistic approximation of the drift-diffusion model

Yang

Yang²

2012

ScienceAsia

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“…The convergence of one-fluid (isentropic) Euler-Maxwell system to compressible Euler-Poisson system is proven via the non-relativistic limit [14]. The cases of two-fluid and non-isentropic are studied by Yang and Wang in [15,16]. Furthermore, paper [17] proves that the combined non-relativistic and quasi-neutral limit of the (isentropic) Euler-Maxwell is the incompressible Euler equations via non-relativistic regime.…”

Section: Introductionmentioning

confidence: 97%

The diffusive relaxation limit of non-isentropic Euler–Maxwell equations for plasmas

Yang

Wang

et al. 2011

Journal of Mathematical Analysis and Applications

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This paper concerns the non-isentropic Euler-Maxwell equations for plasmas with short momentum relaxation time. With the help of the Maxwell-type iteration, it is obtained that, as the relaxation time tends to zero, periodic initial-value problem of certain scaled non-isentropic Euler-Maxwell equations has unique smooth solutions existing in the time interval where the corresponding classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the corresponding drift-diffusion model from the non-isentropic Euler-Maxwell equations.

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“…For the two-fluid Euler-Maxwell equations (1.3), the formal derivation of the limits is done in [15]. The justification of the non-relativistic limit is obtained [17]. The quasi-neutral limit is still open.…”

Section: Introductionmentioning

confidence: 99%

The combined non-relativistic and quasi-neutral limit of two-fluid Euler–Maxwell equations

Peng

2015

Z. Angew. Math. Phys.

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We consider two-fluid Euler-Maxwell equations for magnetized plasmas composed of electrons and ions. By using the method of asymptotic expansions, we analyze the combined non-relativistic and quasi-neutral limit for periodic problems with well-prepared initial data. It is shown that the small parameter problems have a unique solution existing in a finite time interval where the corresponding limit problems (compressible Euler equations) have smooth solutions. The proof is based on energy estimates for symmetrizable hyperbolic equations and on the exploration of the coupling between the Euler equations and the Maxwell equations. Mathematics Subject ClassificationKeywords. Two-fluid Euler-Maxwell system · The combined non-relativistic and quasi-neutral limit · Compressible Euler equations · The asymptotic expansions.

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The non-relativistic limit of Euler–Maxwell equations for two-fluid plasma

Cited by 20 publications

References 17 publications

The combined relaxation and non-relativistic approximation of the drift-diffusion model

The combined relaxation and non-relativistic approximation of the drift-diffusion model

The diffusive relaxation limit of non-isentropic Euler–Maxwell equations for plasmas

The combined non-relativistic and quasi-neutral limit of two-fluid Euler–Maxwell equations

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