Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 4 (September 2021) > Article
VAN DUONG DINH
Université de Lille CNRS
Published on 6 September 2021 DOI : 10.21494/ISTE.OP.2021.0724
In this paper, we consider the following inhomogeneous nonlinear Schrödinger equation (INLS)
||||
with > 0. First, we revisit the local well-posedness in for (INLS) of Guzmán [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. when 0 < < where for , and for
by assuming that the initial data belongs to the weighted space ||. Finally, we combine the local theory and the decaying property to show the scattering in for the defocusing (INLS) in the case < < , where .
In this paper, we consider the following inhomogeneous nonlinear Schrödinger equation (INLS)
||||
with > 0. First, we revisit the local well-posedness in for (INLS) of Guzmán [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. when 0 < < where for , and for
by assuming that the initial data belongs to the weighted space ||. Finally, we combine the local theory and the decaying property to show the scattering in for the defocusing (INLS) in the case < < , where .
Inhomogeneous nonlinear Schrödinger equation Local well-posedness Decay solutions Virial identity Scattering Weighted L2 space
Decay solutions Local well-posedness Inhomogeneous nonlinear Schrödinger equation Virial identity Scattering Weighted L2 space