Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance
Year: 2026
Type: preprint
Abstract: We consider the asymptotic behavior of solutions to inhomogeneous nonlinear Schrödinger equations with non-gauge-invariant nonlinearities. The spatial coefficient in the nonlinear term may have different orders of singularity at the origin and decay at infinity. Under a coercivity condition involving the coefficient and the nonlinearity, we show that no scattering states exist for the equation below a Strauss-type threshold determined by the decay at infinity. Our class includes nonlinearities with a dominant non-oscillatory component. We also prove a complementary small-data scattering result above this threshold, using non-admissible Strichartz estimates in Lorentz spaces adapted to the singular coefficient.
Source: arXiv (Cornell University)
Authors: Grira, Mourad, Miyazaki, Hayato, Tayachi, Slim
Institutions: Tunis El Manar University, Kagawa University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212020206