Analysis & PDE

  • Anal. PDE
  • Volume 1, Number 2 (2008), 229-266.

The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Rowan Killip, Monica Visan, and Xiaoyi Zhang

Full-text: Open access

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut+Δu=±|u|4du for large spherically symmetric Lx2(d) initial data in dimensions d3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.

Article information

Source
Anal. PDE, Volume 1, Number 2 (2008), 229-266.

Dates
Received: 11 August 2008
Revised: 20 August 2008
Accepted: 23 September 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513797961

Digital Object Identifier
doi:10.2140/apde.2008.1.229

Mathematical Reviews number (MathSciNet)
MR2472890

Zentralblatt MATH identifier
1171.35111

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
Nonlinear Schrödinger equation mass-critical focusing

Citation

Killip, Rowan; Visan, Monica; Zhang, Xiaoyi. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. Anal. PDE 1 (2008), no. 2, 229--266. doi:10.2140/apde.2008.1.229. https://projecteuclid.org/euclid.apde/1513797961


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