Smoothing and global attractors for the Hirota-Satsuma system on the torus

Engin Basakoglu*, Tuğrul Bural Gürel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Hirota-Satsuma system, a coupled KdV-type system, with periodic boundary conditions. The first part of the paper concerns with the smoothing estimates for the system. More precisely, it is shown that, for initial data in a Sobolev space, the difference of the nonlinear and linear evolutions lies in a smoother space. The smoothing gain we obtain depends very much on the arithmetic nature of the coupling parameter a which determines the structure of the resonant sets in the estimates. In the second part, we address the forced and damped Hirota-Satsuma system and obtain counterpart smoothing estimates. As a consequence of these estimates, we prove the existence and smoothness of a global attractor in the energy space.
Original languageEnglish
Article number127244
Number of pages34
JournalJournal of Mathematical Analysis and Applications
Volume525
Issue number2
Early online date22 Mar 2023
DOIs
Publication statusPublished - 15 Sept 2023

Keywords

  • Hirota-Satsuma system
  • Smoothing
  • Global attractors

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