发表机构
University of Florida（佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为Maxwell--Ohm演化建立谱弱-强稳定性准则，证明在临界Sobolev指标处稳定性尖锐失效，并构造出Lorentz力收敛到非零测度的反例。
AI 中文摘要
我们在$\nT^d$（$d=2,3$）上建立了具有指定速度的Maxwell--Ohm演化的谱弱-强稳定性准则和尖锐的Sobolev二分法。一致的空间谱紧性，连同每个固定空间Fourier模式的弱收敛以及电磁初始状态的强收敛，推出电磁场的强收敛、电流的弱收敛以及Lorentz力的分布意义收敛。特别地，当$s>d/2$时，速度系数在$L^2_tH^s_x$中的弱收敛就足够了。在临界指标$s=d/2$处，该结论尖锐地失效。我们构造了在临界Sobolev空间中强收敛到零的光滑无散速度，以及强收敛到零的电磁初始状态，而相应的终端场保持为一阶量且电流保持有界。在二维情形中，构造基于移动的对数核；而在三维情形中，它使用由Leray投影格点模和具有精确磁散度约束的极化六分量Maxwell波包构建的Fourier-容量核。在两种维度中，Lorentz力都收敛到一个显式的非零测度，该测度支撑在具有固定单位方向的单条射线上。
英文摘要
We establish a spectral weak-to-strong stability criterion and a sharp Sobolev dichotomy for Maxwell--Ohm evolution with prescribed velocity on $\T^d$, $d=2,3$. Uniform spatial spectral tightness, together with weak convergence of each fixed spatial Fourier mode and strong convergence of the electromagnetic initial states, yields strong convergence of the electromagnetic fields, weak convergence of the currents, and distributional convergence of the Lorentz forces. In particular, weak convergence of the velocity coefficients in $L^2_tH^s_x$ suffices when $s>d/2$. At the critical index $s=d/2$, this conclusion fails sharply. We construct smooth divergence-free velocities converging strongly to zero in the critical Sobolev space, together with electromagnetic initial states converging strongly to zero, while the corresponding terminal fields remain of order one and the currents stay bounded. In two dimensions the construction is based on a moving logarithmic core, whereas in three dimensions it uses a Fourier-capacity core built from Leray-projected lattice modes and a polarized six-component Maxwell packet with exact magnetic divergence constraint. In both dimensions, the Lorentz forces converge to an explicit nonzero measure supported on a single ray with fixed unit direction.
