Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential
Tom 134 / 2014
Colloquium Mathematicum 134 (2014), 143-149
MSC: Primary 35Q55; Secondary 35A15, 35B44.
DOI: 10.4064/cm134-1-7
Streszczenie
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.
