H²-scattering for systems of weakly coupled fourth-order NLS equations in low space dimensions

2018/03/12 by Tarulli, Mirko
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.04182

Abstract

We prove large-data scattering and existence of wave operators in the energy space for the systems of N defocusing fourth-order Schrödinger equations with mass-supercritical and energy-subcritical power-type nonlinearity. In addition, new nonlinear interaction Morawetz identities and inequalities are given, suitable to shed lights on the decay of the solution with respect some Lebesgue norms when the space dimensions are d=3,4.

Related

• Scattering for the focusing, L²-supercritical fourth-order NLS in one dimension
• H¹-scattering for systems of N-defocusing weakly coupled NLS equations in low space dimensions
• Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions
• Scattering for the two-dimensional NLS with (full) exponential nonlinearity
• Decay and Scattering in energy space for the solution of weakly coupled Schrödinger-Choquard and Hartree-Fock equations