STRONG SOLUTIONS TO CAUCHY PROBLEM OF 2D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

This paper studies the local existence of strong solutions to the Cauchy problem of the 2D simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows, coupled via rho (the density of the fluid), u (the velocity of the field), and d (the macroscopic/continuum molecular orientations). Notice that the technique used for the corresponding 3D local well-posedness of strong solutions fails treating the 2D case, because the LP norm (p > 2) of the velocity u cannot be controlled in terms only of rho(1/2)u and Vu here. In the present paper, under the framework of weighted approximation estimates introduced in [J. Li, Z. Liang, On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum, J. Math. Pures Appl. (2014) 640-6711 for Navier-Stokes equations, we obtain the local existence of strong solutions to the 2D compressible nematic liquid crystal flows.