PreprintCC BY 4.0arXiv
On space-time derivative estimates for the magnetohydrodynamic equations
Abstract
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 ∈ Lfqq−3(0,T;Lq (ℝ3)) 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≥1, 2≤ q≤∞ in this system.
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BibTeX
@misc{wang2026spacetime,
title = {{On space-time derivative estimates for the magnetohydrodynamic equations}},
author = {Yanqing Wang and Wei Wei and Gang Wu and Yulin Ye},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12901},
eprint = {2609.12901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12901},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On space-time derivative estimates for the magnetohydrodynamic equations
AU - Yanqing Wang
AU - Wei Wei
AU - Gang Wu
AU - Yulin Ye
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12901
UR - https://arxiv.org/abs/2609.12901
AB - 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 ∈ L^fqq−3(0,T;L^q (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≥1, 2≤ q≤∞ in this system.
ER -