Abstract
In this paper, we prove that every sequence of solutions to the linear Schrödinger equation, with bounded data in H1(Rd), d⩾3, can be written, up to a subsequence, as an almost orthogonal sum of sequences of the type h−(d−2)/2nV((t−tn)/h2n, (x−xn)/ hn ), where V is a solution of the linear Schrödinger equation, with a small remainder term in Strichartz norms. Using this decomposition, we prove a similar one for the defocusing H1-critical nonlinear Schrödinger equation, assuming that the initial data belong to a ball in the energy space where the equation is solvable. This implies, in particular, the existence of an a priori estimate of the Strichartz norms in terms of the energy.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
