Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential

Abstract

Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this threshold can be characterized by polynomial nonlinearities. However, in the critical case, it is difficult to characterize the threshold using only polynomial terms, and thus we use logarithmic nonlinear terms.

References in corpus (4)

• On Kato-Ponce and fractional Leibniz
• Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions
• Critical scattering in a time-dependent harmonic oscillator
• Asymptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials

Cited by in corpus (1)

• Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials