Local well-posedness of the Landau–Lifshitz equation with helicity term

We consider the initial value problem for Landau–Lifshitz equation with a helicity term (chiral interaction term), which arises from Dzyaloshinskii–Moriya energy. prove that it is well-posed locally in-time in space [Formula: see text] s ? 3 and text]. also show if we further assume solution homotopic to constant maps, then local well-posedness holds > 2 Our proof based on two different approaches: One geometric energy method by McGahagan other via modified Schrödinger map equation. In present analysis, exploit special structure of term, enables us overcome difficulty quadratic derivative nonlinearity term.