GLOBAL STRICHARTZ ESTIMATES FOR THE SCHRODINGER EQUATION WITH NON ZERO BOUNDARY CONDITIONS AND APPLICATIONS

被引：13

作者：

Audiard, Corentin ^{[1
]}

机构：

[1] Univ Paris Diderot SPC, Sorbonne Univ, CNRS, Lab Jacques Louis Lions, F-75005 Paris, France

来源：

ANNALES DE L INSTITUT FOURIER | 2019年 / 69卷 / 01期

关键词：

Schrodinger equation; dispersive estimates; boundary conditions; Kreiss-Lopatinskii; compatibility condition; WELL-POSEDNESS; SCATTERING; MANIFOLDS; STABILITY; EXTERIOR;

D O I：

10.5802/aif.3238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Schrodinger equation on a half space in any dimension with a class of nonhomogeneous boundary conditions including Dirichlet, Neuman and the so-called transparent boundary conditions. Building upon recent local in time Strichartz estimates (for Dirichlet boundary conditions), we obtain global Strichartz estimates for initial data in H-s, 0 <= s <= 2 and boundary data in a natural space H-s. For s >= 1/2, the issue of compatibility conditions requires a thorough analysis of the H-s space. As an application we solve nonlinear Schrodinger equations and construct global asymptotically linear solutions for small data. A discussion is included on the appropriate notion of scattering in this framework, and the optimality of the H-s space.

引用

页码：31 / 80

页数：50

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