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

Abstract

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

Revised Version

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Cited by in corpus (1)

• Global existence for the defocusing mass-critical nonlinear fourth-order Schrödinger equation below the energy space