Alphabeta MathResearch collection / 01
Nonlinear Schrödinger equation in an exterior domain
The authors study exact controllability of nonlinear Schrödinger equations outside a smooth nonempty non-trapping obstacle. Internal controls act outside a large ball; the corresponding bounded-domain problem uses Dirichlet controls on the outer sphere. Local smoothing estimates yield linear observability across the Dirichlet Sobolev scale from order −2 to order 2 without requiring the obstacle to be star-shaped.
Combined with dispersive estimates and a perturbation argument, these results give local exact controllability near zero for cubic and quintic equations in dimensions two and three, at Sobolev orders 1 and 2. Internal control near nonzero cubic trajectories requires an additional unique-continuation assumption. The article also discusses extensions and open problems.
Read the original articleResearch & notes
19 entriesPrerequisites
Article items and immediate prerequisites
View the article page dependency graphLevel 0
6 pagesPresents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Presents 29 items from the article and its immediate prerequisites, covering published library prerequisites.
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Presents 29 items from the article and its immediate prerequisites, covering published library prerequisites.
Presents 28 items from the article and its immediate prerequisites, covering published library prerequisites.
Level 1
1 pagePresents 28 items from the article and its immediate prerequisites, covering published library prerequisites and dependency levels 0–1.
Level 2
1 pagePresents 29 items from the article and its immediate prerequisites, covering dependency levels 1–5.
Level 3
1 pagePresents 28 items from the article and its immediate prerequisites, covering dependency levels 5–8.
Level 4
1 pagePresents 29 items from the article and its immediate prerequisites, covering dependency levels 8–10.
Level 5
1 page- Article items · 11 — Partial extension across an artificial sphere and annular cutoff gluing28 items
Presents 28 items from the article and its immediate prerequisites, covering dependency levels 11–15.
Level 6
1 pagePresents 29 items from the article and its immediate prerequisites, covering dependency levels 15–26.