Global Convergence Rates in Zero-Relaxation Limits 
for Non-Isentropic Euler-Maxwell Equations

Tiantian Liu

doi:https://doi.org/10.14445/22315373/IJMTT-V71I7P107

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 7 | Year 2025 | Article Id. IJMTT-V71I7P107 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I7P107

Global Convergence Rates in Zero-Relaxation Limits for Non-Isentropic Euler-Maxwell Equations

Tiantian Liu

Received	Revised	Accepted	Published
24 May 2025	30 Jun 2025	16 Jul 2025	28 Jul 2025

Citation :

Tiantian Liu, "Global Convergence Rates in Zero-Relaxation Limits for Non-Isentropic Euler-Maxwell Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 7, pp. 59-78, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I7P107

Abstract

We analyze the non-isentropic Euler-Maxwell system under small relaxation times for magnetized plasmas and semiconductors. For near-equilibrium smooth periodic initial data, we establish uniform global existence of solutions relative to the relaxation parameter. Crucially, under slow time scaling, these solutions converge globally to the full energy-transport equations as the relaxation time vanishes. Our central innovation provides sharp error estimates between solutions of the non-isentropic system and its energy-transport limit, achieved through novel stream function techniques and enhanced energy methods. This work rigorously bridges these multiscale models while preserving their essential thermo-electromagnetic coupling.

Keywords

Convergence rates, Non-isentropic Euler-Maxwell equations, Energy-transport equations, Stream function.

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