Local well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie stress tensor

摘要

In this paper, we establish the local well-posedness of strong solutions to the Cauchy problem of the density-dependent liquid crystal system, with general Leslie stress tensor, in R-3. By using a biharmonic regularization argument, and making full use of the property of the intrinsic cancellation of the regularized system, we are able to overcome the difficulties caused by the high-order coupling terms, establish some appropriate a priori estimates, which are independent of the regularized parameter, and consequently obtain a strong solution to the original liquid crystal system, by letting the regularization parameter go to zero. The main advantage of the biharmonic regularization is that it does not destroy the property of the intrinsic cancellation of the original system.