发表机构
Zhengzhou University of Light Industry; Northwest University; University of Chinese Academy of Sciences; Henan University（郑州轻工业大学; 西北大学; 中国科学院大学; 河南大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广了Duff对Navier-Stokes系统的先验界至MHD方程，给出时空导数估计，并肯定回答了Zheligovsky提出的问题，同时证明了速度和磁场及其高阶导数的可积性。
AI 中文摘要
本文给出了MHD方程解的时空导数估计。这是Duff在\\(\cite[Acta Math. 164, 1990]{[Duff]}\\)中对经典Navier-Stokes系统先验界的推广，并对Zheligovsky在\\(\cite[Mathematics. 9, 2021]{[Zheligovsky]}\\)中提出的问题给出了肯定回答。此外，我们证明了在该系统中，\\(u, B \in L^{\frac{q}{q-3}}(0,T;L^{q} (\mathbb{R}^{3}))\\)，其中\\(6\leq q\leq \infty\\)，且对于\\(k\geq1, 2\leq q\leq \infty\\)，有\\(D^{k}u, D^{k}B \in L^{\frac{q}{q(k+1)-3}}(0,T;L^{q} (\mathbb{R}^{3}))\\)。
英文摘要
In this paper, we present the space-time derivative estimates of solutions to the MHD equations. It is a generalization of a priori bounds for the classical Navier-Stokes system by Duff in \cite[Acta Math. 164, 1990]{[Duff]} and gives an affirmative answer to a question proposed by Zheligovsky in \cite[Mathematics. 9, 2021]{[Zheligovsky]}. In addition, we show that $u, B \in L^{\f{q}{q-3}}(0,T;L^{q} (\mathbb{R}^{3}))$ with $6\leq q\leq\infty $ and $ D ^{k}u, D ^{k}B \in L^{\f{q}{ q(k+1)-3}}(0,T;L^{q} (\mathbb{R}^{3}))$ for $k\geq1, 2\leq q\leq\infty$ in this system.
