Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
type: Item
instance of: scholarly article
title: Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
zbMATH Open document ID: 1155.35096
author: Benoit Pausader
published in: Dynamics of Partial Differential Equations
publication date: 2008-06-18T00:00:00Z
review text: The author deals with the fourth-order Schrödinger equation of the form \[ i\partial_t u+\Delta^2 u +\varepsilon\Delta u +\lambda| u| ^{p-1}u=0,\quad (x, t)\in {\mathbb R}^{n+1}, \tag \(*\) \] where \(\lambda\in {\mathbb R}\), \(p\in (1, m-1]\), \(m=2n / (n-4)\) is the critical exponent for the embedding of \(H^2\) into Lebesgue's space. The main result is the next Theorem. Let \(n\geq 5\), \(\varepsilon\in {\mathbb R}\), \(\lambda\in {\mathbb R}_+\), and \(p\in (1, m-1]\). For any radially symmetrical data \(u_0\in H^2\) there exists a unique global solution \(u\in C({\mathbb R}; H^2)\) of \((*)\) such that \(u(0)=u_0\).
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 5290376
zbMATH Keywords: energy-critical fourth order Schrödinger equation
zbMATH Keywords: global well-posedness
reviewed by: Georgiĭ Anatol'evich Sviridyuk
MaRDI profile type: Publication
DOI: 10.4310/DPDE.2007.V4.N3.A1
description: scientific article; zbMATH DE number 5290376