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Preprints, Working Papers, ... Year : 2020

Dispersive estimates for the semi-classical Schrödinger equation in a strictly convex domain

Oana Ivanovici

Abstract

We consider a model case for a strictly convex domain $\Omega\subset\mathbb{R}^d$ of dimension $d\geq 2$ with smooth boundary $\partial\Omega\neq\emptyset$ and we describe dispersion for the semi-classical Schrödinger equation with Dirichlet boundary condition. More specifically, we obtain the optimal fixed time decay rate for the linear semi-classical flow : a loss of $(\frac ht)^{1/4}$ occurs with respect to the boundary less case due to repeated swallowtail type singularities. The result is optimal and implies corresponding Strichartz estimates.
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Dates and versions

hal-02950431 , version 1 (28-09-2020)
hal-02950431 , version 2 (26-10-2020)
hal-02950431 , version 3 (17-08-2021)

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Oana Ivanovici. Dispersive estimates for the semi-classical Schrödinger equation in a strictly convex domain. 2020. ⟨hal-02950431v1⟩
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