On the global Cauchy problem for some non linear Schrödinger equations

被引：0

作者：

Ginibre, J. ^{[1
]}

Velo, G. ^{[2
]}

机构：

[1] Laboratoire de Physique Théorique et Hautes Énergies, Université de Paris-Sud, Orsay,91405, France

[2] Dipartimento di Fisica, Università di Bologna and INFN, Sezione di Bologna, Italy

来源：

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire | 1984年 / 1卷 / 04期

关键词：

Partial differential equations;

D O I：

10.1016/S0294-1449(16)30425-5

中图分类号：

学科分类号：

摘要：

We study the Cauchy problem for a class of non linear Schrödinger equations in space time dimension n + 1. We look for solutions which are continuous functions of time with values in the Sobolev space Hk(n), k > n/2. Under suitable assumptions on the interactions, we prove in particular the existence of global solutions for n ≤ 7. The global existence proof breaks down for n ≥ 8. © 2016 L'Association Publications de l'Institut Henri Poincaré

引用

页码：309 / 323

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