WIENER RANDOMIZATION ON UNBOUNDED DOMAINS AND AN APPLICATION TO ALMOST SURE WELL-POSEDNESS OF NLS

By 'Arp'ad B'enyi, Tadahiro Oh, Oana Pocovnicu. 2014

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We introduce a randomization of a function on \( \mathbb{R}^{d} \) that is naturally associated to the Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized functions enjoy better integrability, thus allowing us to improve the Strichartz estimates for the Schrodinger equation. As an example, we also show that the energy-critical cubic nonlinear Schrodinger equation on \( \mathbb{R}^{4} \) is almost surely locally well posed with respect to randomized initial data below the energy space.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3cf9dc8ac6861f5a88fbd038184b77998f178c2b