Local well-posedness for the $H^2$-critical nonlinear Schrödinger equation

Abstract

In this paper, we consider the nonlinear Schrödinger equation $i{u}_t+\Delta u=\lambda |u{|}^{\frac{4}{N-4}}u$ in ${\mathbb{R}}^N$, $N\ge 5$, with $λ\in \C$. We prove local well-posedness (local existence, unconditional uniqueness, continuous dependence) in the critical space ${\dot{H}}^2({\mathbb{R}}^N)$.

References in corpus (1)

• Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^s$