Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D
Abstract
We construct global finite-energy weak solutions for a 1D barotropic Navier--Stokes--Maxwell system with displacement current and the algebraic Ohm law. The result holds for every γ>1 and arbitrary finite-energy initial data, allowing vacuum and requiring only L2 initial electromagnetic fields. A key ingredient is a weak-to-strong compactness principle for the Maxwell--Ohm subsystem: weak convergence of the velocity coefficients in L2tH1x, together with strong convergence of the initial fields, yields strong electromagnetic trajectories in CtL2x. This permits identification of the weak current and the distributional Lorentz force without strong convergence of the velocity. The electromagnetic closure is combined with the classical artificial-viscosity and artificial-pressure construction for compressible flow. A density-primitive effective-flux argument identifies the physical pressure and eliminates the physical and artificial pressure-concentration defects.
Related
- Optimal Time-Decay of global solutions to the Navier-Stokes-Maxwell system
- Global well-posedness and Decay estimates for solutions of the Navier--Stokes--Maxwell system
- Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
- Endpoint Compactness and Finite-Energy Weak Solutions for the 2D Isothermal Compressible Navier-Stokes
- Compactly Supported Finite-Energy Stationary Solutions of the Three-Dimensional Navier-Stokes Equations
BibTeX
@misc{yu2026global,
title = {{Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D}},
author = {Cheneg Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24960},
eprint = {2609.24960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24960},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D
AU - Cheneg Yu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24960
UR - https://arxiv.org/abs/2609.24960
AB - We construct global finite-energy weak solutions for a 1D barotropic Navier--Stokes--Maxwell system with displacement current and the algebraic Ohm law. The result holds for every γ>1 and arbitrary finite-energy initial data, allowing vacuum and requiring only L^2 initial electromagnetic fields. A key ingredient is a weak-to-strong compactness principle for the Maxwell--Ohm subsystem: weak convergence of the velocity coefficients in L^2_tH^1_x, together with strong convergence of the initial fields, yields strong electromagnetic trajectories in C_tL^2_x. This permits identification of the weak current and the distributional Lorentz force without strong convergence of the velocity. The electromagnetic closure is combined with the classical artificial-viscosity and artificial-pressure construction for compressible flow. A density-primitive effective-flux argument identifies the physical pressure and eliminates the physical and artificial pressure-concentration defects.
ER -