Asian Research Journal of Mathematics

This work establishes the global-in-time convergence when the light speed c → ∞ (ν = \(\frac1c\) → 0), demonstrating how the non-isentropic Euler-Maxwell system reduces to the Euler-Poisson system near non-constant equilibria. The non-isentropic setting introduces new challenges due to temperature effects and energy coupling, complicating dissipation estimates for the electric field E. A div-curl decomposition is required, disrupting the system’s anti-symmetric structure and L²-estimates. By constructing a tailored strictly convex entropy functional and employing refined induction arguments, we establish global convergence. Key to our analysis is the non-singularity of E under non-relativistic scaling, alongside novel estimates for thermal-electromagnetic interactions.