Abstract
In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schrödinger equation
with \(b, \alpha >0\). We first study the decaying property of global solutions for the equation when \(0<\alpha <\alpha ^\star \) where \(\alpha ^\star = \frac{4-2b}{d-2}\) for \(d\ge 3\). The proof makes use of an argument of Visciglia (Math Res Lett 16(5):919–926, 2009). We next use this decay to show the energy scattering for the equation in the case \(\alpha _\star<\alpha <\alpha ^\star \), where \(\alpha _\star = \frac{4-2b}{d}\).
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Dinh, V.D. Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation. J. Evol. Equ. 19, 411–434 (2019). https://doi.org/10.1007/s00028-019-00481-0
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DOI: https://doi.org/10.1007/s00028-019-00481-0