Scattering in the Energy Space for the Damped Nonlinear Fourth-Order Schrödinger Equation in Higher Dimensions Under Spherical Symmetry
Year: 2025
Type: article
Abstract: We establish global decay and scattering in the energy space H2(Rd), for d≥5, of radial solutions to the damped nonlinear biharmonic Schrödinger equation with general complex-valued, time-dependent damping coefficients. Assuming radial data exploits O(d)-symmetry and strengthens Morawetz-type controls through spherical averaging, we introduce new Morawetz-type identities and localized inequalities adapted to the fourth-order dispersive flow and compatible with this symmetry. As a consequence, and under explicit conditions for the damping coefficients that include slowly decaying or oscillatory profiles, we prove that solutions decay in Lebesgue norms and scatter to free biharmonic evolutions.
Source: Symmetry
DOI: 10.3390/sym17091541
Author: Mirko Tarulli
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4414205222