On the defect of compactness for the Strichartz estimates of the Schrodinger equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:175

Article

Keraani, S

关键词: Schrodinger equations;    Strichartz estimates;    compactness;    asymptotic analysis;    a priori estimates;   

DOI  :  10.1006/jdeq.2000.3951

来源: Elsevier

【 摘 要 】

In this paper, we prove that every sequence of solutions to the linear Schrodinger equation, with bounded data in H-1(R-d), d greater than or equal to 3, can be written, up to a subsequence, as an almost orthogonal sum of sequences of the type h(n)(-(d-2)/2) V((t-t(n))/h(n)(2), (x-x(n))/h(n)), where V is a solution of the linear Schrodinger equation, with a small remainder term in Strichartz norms. Using this decomposition, we prove a similar one for the defocusing H-1-critical nonlinear Schrodinger 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, (C) 2001 Academic Press.

【 授权许可】

Free