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

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

We study the two-dimensional periodic nonlinear Schr\"odinger equation (NLS) with the quadratic nonlinearity $|u|^2$. In particular, we study the quadratic NLS with random initial data distributed according to a fractional derivative (of order $\alpha \geq 0$) of the Gaussian free field. After...

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Bibliographische Detailangaben
1. Verfasser:	Liu, Ruoyuan
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Analysis of PDEs Mathematics - Probability
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