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>

Abstract

In this paper, for a nematic liquid crystal system, we address the space-time decay properties of strong solutions in the whole space R 3 . Based on a parabolic interpolation inequality, bootstrap argument and some weighted estimates, we obtain the higher order derivative estimates for such system. 2000 Mathematics Subject Classification. Primary: 35Q35, 35B40; Secondary: 35D35.

Asymptotic behavior of solutions to incompressible electron inertial Hall-MHD system in $ \mathbb{R}^3 $

“…Latterly, Miyakawa [22] and Kukavica [18] established the sharp space-time decay rate for Navier-Stokes equations; Kukavica and Torres [20] established the sharp rates of decay for any weighted norm of higher order. Recently, Weng [29,30] addressed the space-time decay properties for higher-order derivatives of strong solutions to the incompressible viscous resistive Hall-MHD equations and viscous Boussinesq system in the usual Sobolev space, Zhao [33] studied the space-time decay of strong solutions to liquid crystal system.…”