  We study the Ericksen-Leslie system equipped with a quadratic free energy
functional. The norm restriction of the director is incorporated by a standard
relaxation technique using a double-well potential. We use the relative energy
concept, often applied in the context of compressible Euler- or related systems
of fluid dynamics, to prove weak-strong uniqueness of solutions. A main novelty
is that the relative energy inequality is proved for a system with a nonconvex
energy.

Analysis of PDEs