Smoothing and global attractors for the Hirota-Satsuma system on the torus
Journal of Mathematical Analysis and Applications, cilt.525, sa.2, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 525 Sayı: 2
- Basım Tarihi: 2023
- Doi Numarası: 10.1016/j.jmaa.2023.127244
- Dergi Adı: Journal of Mathematical Analysis and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
- Anahtar Kelimeler: Global attractors, Hirota-Satsuma system, Smoothing
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.