Global smoothing for the Davey–Stewartson system on ℝ2

Engin Basakoglu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number34
Number of pages25
JournalJournal of Evolution Equations
Volume22
Issue number2
Early online date18 Apr 2022
DOIs
Publication statusPublished - Jun 2022

Keywords

  • Davey–Stewartson system
  • Global smoothing
  • Global attractors

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