Regularity and decay rates of solutions to n-dimensional generalized magnetohydrodynamic equations

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发表日期：

2026年2月12日

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Cung The Anh,
Trinh Dang Duong,
Vu Manh Toi

摘要

This paper studies the regularity and large time behavior of global solutions to the n-dimensional generalized magnetohydrodynamic equations on the whole space. First, we prove the existence and regularity of global solutions with small initial data. After that, we show that the solutions converge to zero in $L^2$ $L^{2}$ -norm. However, there is no uniform decay rate when the initial data only belong to $L^2$ $L^{2}$ . Finally, we use the notion of decay indicator and decay character to characterize the decay rates in $L^2$ $L^{2}$ -norm of these solutions and their higher-order derivatives in terms of initial data.