$Sharp local well-posedness of the two-dimensional periodic nonlinear Schr\"odinger equation with a quadratic nonlinearity $|u|^2$

Sharp local well-posedness of the two-dimensional periodic nonlinear Schr\"odinger equation with a quadratic nonlinearity $|u|^2

We study the nonlinear Schr\"odinger equation (NLS) with the quadratic nonlinearity $|u|^2$, posed on the two-dimensional torus $\mathbb{T}^2$. While the relevant $L^3$-Strichartz estimate is known only with a derivative loss, we prove local well-posedness of the quadratic NLS in $L^2(\mathbb{T...

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Bibliographische Detailangaben
Hauptverfasser:	Liu, Ruoyuan, Oh, Tadahiro
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Analysis of PDEs
Online-Zugang:	Volltext bestellen
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