Energy concentration of the focusing energy-critical fNLS

Abstract

We consider the fractional nonlinear Schrodinger equation (fNLS) with non-local dispersion vertical bar del vertical bar(alpha) and focusing energy-critical Hartree type nonlinearity [-(vertical bar x vertical bar(-2 alpha) * vertical bar u vertical bar(2))u]. We consider the energy -concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration -compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case. (C) 2015 Elsevier Inc. All rights reserved.