Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415127 | Journal of Functional Analysis | 2014 | 38 Pages |
Abstract
We consider the question of global existence of small, smooth, and localized solutions of a certain fractional semilinear cubic NLS in one dimension,iâtuâÎu=c0|u|2u+c1u3+c2uu¯2+c3u¯3,Î=Î(âx)=|âx|12, where c0âR and c1,c2,c3âC. This model is motivated by the two-dimensional water wave equation, which has a somewhat similar structure in the Eulerian formulation, in the case of irrotational flows. We show that one cannot expect linear scattering, even in this simplified model. More precisely, we identify a suitable nonlinear logarithmic correction, and prove global existence and modified scattering of solutions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexandru D. Ionescu, Fabio Pusateri,