Local well-posedness for the 𝐻²-critical nonlinear Schrödinger equation

Cazenave, Thierry; Fang, Daoyuan; Han, Zheng

doi:10.1090/tran6683

Local well-posedness for the $H^2$-critical nonlinear Schrödinger equation
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Trans. Amer. Math. Soc. 368 (2016), 7911-7934 Request permission

Abstract:

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

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