Global stability of large steady-states for an isentropic Euler–Maxwell system in $\mathbb{R}^3$

Liu, Cunming; Guo, Zuji; Peng, Yue‐Jun

doi:10.4310/cms.2019.v17.n7.a4

Cited by 8 publications

(2 citation statements)

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“…After that, by the similar way, Feng, Peng, and Wang; Feng, Wang, and Li; and Li, Wang, and Feng considered the stability problems for the 2‐fluid isentropic case, 1‐fluid, and 2‐fluid nonisentropic cases with temperature diffusion terms, respectively. Recently, with the help of choosing a new symmetrizer matrix, the stability of the 1‐fluid nonisentropic Euler‐Poisson system is considered . However, there is no result on the stability of nonconstant equilibrium solutions for the 2‐fluid nonisentropic Euler‐Poisson systems without temperature diffusion effects so far.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability of nonconstant steady‐state solutions for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor

Wang

Feng

2018

Math Methods in App Sciences

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Beijing project of scientific activities for the excellent students studying abroad ; Beijing University of Technology foundation funded project MSC Classification: 35L45; 35L60; 35L65; 35Q60; 76×05 We consider the periodic problem for 2-fluid nonisentropic Euler-Poisson equations in semiconductor. By choosing a suitable symmetrizers and using an induction argument on the order of the time-space derivatives of solutions in energy estimates, we obtain the global stability of solutions with exponential decay in time near the nonconstant steady-states for 2-fluid nonisentropic Euler-Poisson equations. This improves the results obtained for models with temperature diffusion terms by using the pressure functions p in place of the unknown variables densities n . KEYWORDS 2-fluid nonisentropic Euler-Poisson equations, global smooth solutions, nonconstant steady-state solutions, semiconductor 3588

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability of nonconstant steady‐state solutions for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor

Wang

Feng

2018

Math Methods in App Sciences

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“…For a function n satisfying

n - 1 \in H^{s} false(R^{d} false)

and n ≥ const. > 0, it is proved that (see Hsiao et al and Liu et al) the Poisson equation

- λ^{2} normalΔ ϕ + e^{ϕ} = n

admits a unique solution ϕ such that

e^{ϕ} - n \in H^{s} false(R^{d} false)

. Moreover, as n is sufficiently close to 1, ϕ is sufficiently close to 0.…”

Section: Introductionmentioning

confidence: 98%

Global convergence of the Euler‐Poisson system for ion dynamics

Liu

Peng

2018

Math Methods in App Sciences

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We consider smooth solutions of the Euler‐Poisson system for ion dynamics in which the electron density is replaced by a Boltzmann relation. The system arises in the modeling of plasmas, where appear two small parameters, the relaxation time and the Debye length. When the initial data are sufficiently close to constant equilibrium states, we prove the convergence of the system for all time, as each of the parameters goes to zero. The limit systems are drift‐diffusion equations and compressible Euler equations. The proof is based on uniform energy estimates and compactness arguments.

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From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass

Xi,

Zhao

2024

J. Math. Fluid Mech.

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Global stability of large steady-states for an isentropic Euler–Maxwell system in $\mathbb{R}^3$

Cited by 8 publications

References 0 publications

Stability of nonconstant steady‐state solutions for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor

Stability of nonconstant steady‐state solutions for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor

Global convergence of the Euler‐Poisson system for ion dynamics

From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass

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