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- W4353056918 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." @default.
- W4353056918 created "2023-03-23" @default.
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- W4353056918 date "2023-09-01" @default.
- W4353056918 modified "2023-10-16" @default.
- W4353056918 title "Smoothing and global attractors for the Hirota-Satsuma system on the torus" @default.
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- W4353056918 doi "https://doi.org/10.1016/j.jmaa.2023.127244" @default.
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