2018/03/23 by Victor Chabu, Clotilde Fermanian Kammerer, Chabu, Victor +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.1803.08771
openalex publication_date 2018/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schrödinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time semiclassical limit within this non compact geometry and exhibit conditions under which the energy remains localized on compact sets. We also explain how our results can be applied in a straightforward way to describe obstructions to the validity of smoothing type estimates.