The Ericksen-Leslie System for Data on a Plane

The work deals with the Ericksen-Leslie system for nematic liquid crystals on the whole space with dimension greater or equal than 3. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence with decay in time for small initial data of a solution in Sobolev spaces asking low regularity for the initial conditions.