Local smoothing estimates of fractional Schr\'odinger equations in $\alpha$-modulation spaces with some applications

Autor:	Lu, Yufeng
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs 35R11 35Q55 42B37
Druh dokumentu:	Working Paper
Popis:	We show some new local smoothing estimates of the fractional Schr\"odinger equations with initial data in $\alpha$-modulation spaces via decoupling inequalities. Furthermore, our necessary conditions show that the local smoothing estimates are sharp in some cases. As applications, the local smoothing estimates could show some new local well-posedness on modulation spaces of the fourth-order nonlinear Schr\"odinger equations on the line. Comment: 30 pages, 3 figures, all comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.06596 Zobrazit plný text záznamu View this record from Arxiv