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Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential

Volume 134 / 2014

Xing Cheng, Yanfang Gao Colloquium Mathematicum 134 (2014), 143-149 MSC: Primary 35Q55; Secondary 35A15, 35B44. DOI: 10.4064/cm134-1-7

Abstract

The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential \[ {\mathrm i}\partial_t u + \tfrac{1}{2}\varDelta u - \tfrac12 |x|^2 u = -|u|^{4/(d-2)}u, \quad x \in \mathbb R^d, \] is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.

Authors

  • Xing ChengDepartment of Mathematics
    University of Science and Technology of China
    Hefei 230026, China
    e-mail
  • Yanfang GaoSchool of Mathematics
    and Computer Science
    Fujian Normal University
    Fuzhou, China, 350117
    e-mail

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