Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.11199

From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit

Immanuel Ben Porat
View original source ↗Read source document ↗Export metadata ↓

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

Explore related subjects

math.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Immanuel Ben Porat. 2026-10-08. From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit. https://arxiv.org/abs/2610.11199

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Explicit lower bound of blow-up time in a fully parabolic attraction-repulsion chemotaxis system with nonlinear terms

It is known that for the parabolic-elliptic Keller-Segel type system in a smooth bounded domain in 3-dimensional space, the lower bound of a blow-up time of unbounded solution is given. This paper extends the previous works to deal with the fully parabolic Keller-Segel type system in any spatial dimension larger than 3. Firstly, we prove that any blow-up time of an energy function is also the classical blow-up time when its energy level is sufficiently large. Secondly, we give an explicit estimation for the lower bound of blow-up time for the fully parabolic attraction-repulsion chemotaxis system with nonlinear terms, under homogeneous Neumann boundary conditions, in a smooth bounded domain.

math.AP↗
arXiv2026

Regularity and positivity of solutions of the Consensus-Based Optimization equation: unconditional global convergence

Introduced in {\it R. Pinnau, et al. (Math. Models Methods Appl. Sci., 2017)}, Consensus-Based Optimization (CBO) has rapidly emerged as a significant breakthrough in global optimization. This straightforward yet powerful multi-particle, zero-order optimization method draws inspiration from Simulated Annealing and Particle Swarm Optimization. Using a quantitative mean-field approximation, CBO dynamics can be described by a nonlinear Fokker-Planck equation with degenerate diffusion, which does not follow a gradient flow structure. In this paper, we demonstrate that solutions to the CBO equation remain positive and maintain full support. Building on this foundation, we establish the {\it unconditional} global convergence of CBO methods to global minimizers. Our results are derived through an analysis of solution regularity and the proof of existence for smooth, classical solutions to a broader class of drift-diffusion equations, despite the challenges posed by degenerate diffusion.

math.AP↗
arXiv2026

An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data

We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to investigate, for the 1+1 dimensional model, how jump discontinuities on the boundary and initial data influence the regularity of both the solution and the free boundary. We show that if the data is merely bounded, then weak solutions are Lipschitz in space and $C^{1/2}$ in time in the unsaturated region. Moreover, the free boundary is locally the graph of a $C^{1/2}$ function, and this regularity is optimal. We view this analysis as a stepping stone towards the study of local regularization for higher-dimensional elliptic-parabolic free boundaries.

math.AP↗