发表机构
Shanghai Jiao Tong University; Zhejiang Sci-Tech University; Shanghai Lixin University of Accounting and Finance（上海交通大学; 浙江理工大学; 上海立信会计金融学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维可压缩磁流体力学方程，构造了全局弱解和强解，通过密度矩与重整化技术实现弱-强唯一性，并给出压力指数的下确界。
AI 中文摘要
我们研究了具有常数剪切粘性和磁扩散系数、体积粘性为$\rho^\beta$、压力为$\rho^\gamma$的二维周期可电阻性可压缩磁流体力学方程。对于每个$\beta>1$和$\gamma>1$，我们从严格正有界$W^{1,q}$密度（$q>2$）和任意$H^1$速度及磁场数据出发，构造了全局有限能量重整化弱解。该构造结合了与近似无关的有限密度矩、广义有效通量恒等式，以及密度及其熵亏损的联合对数重整化。包含$\beta$幂密度势的增广相对能量，在相同的完整压力范围内，针对正$H^2$强解产生了弱-强唯一性。当$\gamma>\max\{5-2\beta,\beta+1\}$时，我们还为大背景族建立了全局强解存在性。记$m=\int\rho_0$，密度扰动在缩放范数$m^{(\gamma-3)/2}\\|\rho_0-m\\|_{H^2}$下有界，而固定的$H^2$速度和磁场范数不必很小。对于足够大的$m$，频率相关的声学耗散、分阶段涡量权重和单独的初始层通量估计闭合了同步自举。允许的压力指数下确界为$7/3$，端点被排除。对于$\beta>2$，相关阻尼率是粘性率和压力松弛率的最小值；保持两个速率可在$\beta$上没有上限限制的情况下扩展论证。强定理在此缩放密度假设下对$\gamma$没有上限限制；对于固定的加性密度扰动，它在所述较低范围内适用，直至$\gamma=3$。
英文摘要
We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity $ρ^β$, and pressure $ρ^γ$. For every $β>1$ and $γ>1$, we construct global finite-energy renormalized weak solutions from strictly positive bounded $W^{1,q}$ densities, $q>2$, and arbitrary $H^1$ velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the $β$-power density potential yields weak--strong uniqueness against positive $H^2$ strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when $γ>\max\{5-2β,β+1\}$. Writing $m=\intρ_0$, the density perturbation is bounded in the scaled norm $m^{(γ-3)/2}\|ρ_0-m\|_{H^2}$, while the fixed $H^2$ velocity and magnetic norms need not be small. For sufficiently large $m$, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum $7/3$, with the endpoint excluded. For $β>2$ the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on $β$. The strong theorem has no upper restriction on $γ$ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to $γ=3$.
Comments59 pages
