Long Time Dynamics of Nonradial Solutions to Inhomogeneous Nonlinear Schrödinger Equations
Abstract
We study long time dynamics of nonradial solutions to the focusing inhomogeneous nonlinear Schrödinger equation. By using the concentration/compactness and rigidity method, we establish a scattering criterion for nonradial solutions to the equation. We also prove a nonradial blow-up criterion for the equation whose proof makes use of localized virial estimates. As a byproduct of these criteria, we study long time dynamics of nonradial solutions to the equation with data lying below, at, and above the ground state threshold. In addition, we provide a new argument showing the existence of finite time blow-up solution to the equation with cylindrically symmetric data. The ideas developed in this paper are robust and can be applicable to other types of nonlinear Schrödinger equations.
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4765 - 4811
DOI: 10.1137/20M1383434
ISSN (online): 1095-7154
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© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 30 November 2020
Accepted: 10 May 2021
Published online: 26 August 2021
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Agence Nationale de la Recherche https://doi.org/10.13039/501100001665 : ANR-11-LABX-0007-01
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