The well-posedness of nonlinear Schrödinger equations in Triebel-type spaces

Shaolei Ru and Jiecheng Chen

Vol. 274 (2015), No. 2, 325–354

DOI: 10.2140/pjm.2015.274.325

Abstract

Sufficient and necessary conditions for embeddings between $F_{p,q}^s$ (Triebel spaces) and $N_{p,q}^s$ (new spaces constructed by combining frequency-uniform decomposition with $L^{‘p}\left({\ell }^q\right)$) are obtained. Moreover, we study the Cauchy problem for generalized nonlinear Schrödinger equations in $L^r\left(0,T,N_{p,q}^s\right)$.

Keywords

nonlinear Schrödinger equation, embedding between Triebel spaces and $N_{p,q}^{s}$, dual estimate

Mathematical Subject Classification 2010

Primary: 42B37, 42B35, 35Q55

Milestones

Received: 9 November 2013

Revised: 13 May 2014

Accepted: 11 September 2014

Published: 1 April 2015