Geodesic
Dispersive estimates for the Schrödinger equation in a model convex domain and applications
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 4, pp. 959-1008

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We consider an anisotropic model case for a strictly convex domain Ω⊂ℝ d of dimension d≥2 with smooth boundary ∂Ω≠∅ and we describe dispersion for the semiclassical Schrödinger equation with Dirichlet boundary condition. More specifically, we obtain the following fixed time decay rate for the linear semiclassical flow: a loss of (h t) 1/4 occurs with respect to the boundaryless case due to repeated swallowtail-type singularities, and is proven optimal. Corresponding Strichartz estimates allow us to solve the cubic nonlinear Schrödinger equation on such a three-dimensional model convex domain, hence matching known results on generic compact boundaryless manifolds.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/75
Classification : 35J25
Keywords: Cubic Schrödinger equation, boundary problems, dispersive and Strichartz estimates 
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     author = {Ivanovici, Oana},
     title = {Dispersive estimates for the {Schr\"odinger} equation in a model convex domain and applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {959--1008},
     volume = {40},
     number = {4},
     year = {2023},
     doi = {10.4171/aihpc/75},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/75/}
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Ivanovici, Oana. Dispersive estimates for the Schrödinger equation in a model convex domain and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 4, pp. 959-1008. doi: 10.4171/aihpc/75

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