Well-posedness of the full Ericksen-Leslie model of nematic liquid crystals - Coutand, D; Shkoller, S (2001)
The Ericksen-Leslie model of nematic liquid crystals is a coupled system between the Navier-Stokes and the Ginzburg-Landau equations. We show here the local well-posedness for this problem for any initial data regular enough, by a fixed point approach relying on some weak continuity properties in a suitable functional setting. By showing the existence of an appropriate local Lyapunov functional, we also give sufficient conditions for the global existence of the solution, and some stability conditions. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.