Time decay rate for two 3D magnetohydrodynamics- α models

Abstract

We consider the long time behavior of solutions to the magnetohydrodynamics‐ α model in three spatial dimensions. Time decay rate in L2‐norm of the solution is obtained. Similar results for a generalized Leray‐ α‐magnetohydrodynamics model are also established. As a by‐product, an optimal time decay rate for the Navier–Stokes‐ α model is achieved. Copyright © 2013 John Wiley & Sons, Ltd.

Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations

“…Their method provides a very simple derivation of Wiegner's fundamental results (see [30]). One can refer to [36,9,10] for details and developments.…”

Space-time decay estimates of solutions to liquid crystal system in <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^3$\end{document}</tex-math></inline-formula>

“…We point out that Zhou introduced a new method (see [36], some people called Zhou's method) to handle decay rate problems. One can refer to [37,14,15] for details and developments.…”