Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D

Cheneg Yu

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arXiv · 2609.24960

Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D

Cheneg Yu

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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 $L^2$ 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.

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Cheneg Yu. 2026-09-21. Global finite-energy weak solutions to the Navier--Stokes--Maxwell in 1D. https://arxiv.org/abs/2609.24960

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