From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit
Year: 2026
Type: preprint
Abstract: We derive the pressureless Euler-Maxwell system as a semiclassical limit from the Maxwell-Schrödinger equation. The method relies on studying a quantum modulated energy accounting for the self-consistent magnetic effects. Crucially, a correction is incorporated in the quantum modulated energy as to enable to close the Grönwall estimate provided a smallness assumption on the initial data is imposed. This is the first result on the semiclassical limit of the Maxwell-Schrödinger equation avoiding any regularization or conditional uniform in $\hbar$ bounds on the wave
Source: arXiv (Cornell University)
Author: Porat, Immanuel Ben
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221137230