Abstract
In this paper, we study the regularity properties of solutions to the Davey–Stewartson system. It is shown that for initial data in a Sobolev space, the nonlinear part of the solution flow resides in a smoother space than the initial data for all times. We also obtain that the Sobolev norm of the nonlinear part of the evolution grows at most polynomially. As an application of the smoothing estimate, we study the long-term dynamics of the forced and weakly damped Davey–Stewartson system. In this regard, we give a new proof for the existence and smoothness of the global attractors in the energy space.
Original language | English |
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Article number | 34 |
Number of pages | 25 |
Journal | Journal of Evolution Equations |
Volume | 22 |
Issue number | 2 |
Early online date | 18 Apr 2022 |
DOIs | |
Publication status | Published - Jun 2022 |
Keywords
- Davey–Stewartson system
- Global smoothing
- Global attractors