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arXiv · 1504.06438

Almost sure local wellposedness of energy critical fractional Schr\"odinger equations with hartree nonlinearity

Gyeongha Hwang
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Abstract

We consider a Cauchy problem of energy-critical fractional Schr\"odinger equation with Hartree nonlinearity below the energy space. Using a method of randomization of functions on $\mathbb{R}^d$ associated with the Wiener decomposition, introduced by \'{A}. B\'{e}nyi, T. Oh, and O. Pocovnicu \cite{beohpo1,beohpo2}, we prove that the Cauchy problem is almost surely locally well-posed. Our result includes Hartree Schr\"odinger equation ($\alpha = 2$).

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Gyeongha Hwang. 2015-04-24. Almost sure local wellposedness of energy critical fractional Schr\"odinger equations with hartree nonlinearity. https://arxiv.org/abs/1504.06438

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