The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrodinger equation

被引：8

作者：

Lee, Yoonjung ^{[1
]}

Seo, Ihyeok ^{[1
]}

机构：

[1] Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea

来源：

ARCHIV DER MATHEMATIK | 2021年 / 117卷 / 04期

关键词：

Well-posedness; Nonlinear Schrodinger equations; Weighted estimates; WELL-POSEDNESS; REGULARITY; DECAY;

D O I：

10.1007/s00013-021-01632-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the Cauchy problem for the energycritical inhomogeneous nonlinear Schrodinger equation i partial derivative(t)u + Delta u = lambda vertical bar x vertical bar(-alpha)vertical bar u vertical bar(beta) u in H-1. The well-posedness theory in H-1 has been intensively studied in recent years, but the currently known approaches do not work for the critical case beta = (4 - 2 alpha)/(n - 2). It is still an open problem. The main contribution of this paper is to develop the theory in this case.

引用

页码：441 / 453

页数：13

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