Local well-posedness to the 2D Cauchy problem of non-isothermal nonhomogeneous nematic liquid crystal flows with vacuum at infinity

Abstract

<p style='text-indent:20px;'>This paper concerns the Cauchy problem of non-isothermal nonhomogeneous nematic liquid crystal flows in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula> with zero density at infinity. By spatial weighted energy method and a Hardy type inequality, we show the local existence and uniqueness of strong solutions provided that the initial density and the gradient of orientation decay not too slowly at infinity.</p>