DOI: 10.1515/anona-2025-0193 ISSN: 2191-950X

On the global solvability and asymptotic stability for Schrödinger–Boussinesq–type systems

Carlos Banquet, Lucas C. F. Ferreira, Élder J. Villamizar-Roa
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Abstract

This paper is devoted to the solvability of nonlinear Schrödinger–Boussinesq–type systems in the framework of weak- L p spaces, exploring the nonlocal effect of time-fractional evolution and the Lévy trajectories in the model. We prove the existence of local and global mild solutions, as well as the asymptotic stability, considering polynomial-type nonlinearities, and initial data in weak- L p spaces. As a consequence of the embedding of weak- L p spaces in

L loc 2 ${L}_{\text{loc}}^{2}$
, for p > 2, the obtained solutions have finite local L 2 -mass. We also derive the existence of local and global solutions in the same framework for the nonlinear time-space fractional dispersive Boussinesq equation.

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