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

Thierry Cazenave (1) , Daoyuan Fang (2) , Zheng Han (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Department of Mathematics [Hangzhou]

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

Mots clés: unconditional uniqueness; local existence; continuous dependence; $H^2$-critical nonlinear Schrödinger equation

Domaines: Equations aux dérivées partielles [math.AP]

Thierry Cazenave, Daoyuan Fang, Zheng Han. Local well-posedness for the $H^2$-critical nonlinear Schrödinger equation. Transactions of the American Mathematical Society, 2016, 368 (11), pp.7911-7934. ⟨10.1090/tran6683⟩. ⟨hal-00907000⟩