Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds

DOI10.1137/22m1529312arXiv2111.09651MaRDI QIDQ6202904

Zehua Zhao, Haitian Yue, Xueying Yu

Publication date: 27 February 2024

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.09651

zbMATH Keywords

scatteringwell-posednessStrichartz estimatefourth-order Schrödinger equationinteraction Morawetz estimatewaveguide manifold

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

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