Global well-posedness for a $L^2$-critical nonlinear higher-order Schrödinger equation

International audienceWe prove the global well-posedness for a $L^2$-critical defocusing cubic higher-order Schrödinger equation, namely $i\partial_tu + \Lambda^k u = −|u|^2 u$, where $\Lambda = \sqrt{-\Delta}$ and $k \geq 3, k \in \mathbb{Z}$ in $R^k$ with initial data $u_0 \in H^\gamma, \gamma > \gamma(k) := \frac{k(4k−1)}{14k−3}$