On the focusing energy-critical fractional nonlinear Schrödinger equations
The authors consider the fractional nonlinear Schrödinger equation (FNLS) with non-local dispersion \(|\nabla|^\alpha\) and focusing energy-critical Hartree type nonlinearity \(-(| x|^{-2\alpha}\ast| u|^2)u\). They establish the global well-posedness for the radial case in energy space when the initial energy and initial kinetic energy are less than those of the ground state, respectively. Moreover, they prove finite time blowup via commutator techniques.
scientific article; zbMATH DE number 6822197