On <inline-formula><tex-math id="M1">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> estimates for a simplified Ericksen-Leslie system

Abstract

In this paper, we study Cauchy problem for a simplified Ericksen-Leslie system in three dimensions. With the initial data of small perturbation near a steady state in \begin{document}$ H^2 $\end{document} norm, we obtain the global well-posedness of strong solutions as well as the \begin{document}$ L^p(p\in[1, 6]) $\end{document} estimates. In addition, sharper decay rates for the density and the momentum are obtained.