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arXiv · 2101.09423

Modified scattering for inhomogeneous nonlinear Schr\"odinger equations with and without inverse-square potential

Kazuki Aoki·Takahisa Inui·Hayato Miyazaki·Haruya Mizutani·Kota Uriya
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Abstract

We consider the final state problem for the inhomogeneous nonlinear Schr\"odinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a logarithmic phase correction compared with the free evolution, we construct a unique global solution which converges to the profile. As a consequence, the existence of modified wave operators for localized small scattering data is obtained. We also study the same problem for the case with the critical inverse-square potential under the radial symmetry. In particular, we construct the modified wave operators for the long-range nonlinear Schr\"odinger equation with the critical inverse-square potential in three space dimensions, under the radial symmetry.

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Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani, Kota Uriya. 2021-01-23. Modified scattering for inhomogeneous nonlinear Schr\"odinger equations with and without inverse-square potential. https://arxiv.org/abs/2101.09423

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