On the decay and Gevrey regularity of the solutions to the Navier-Stokes equations in general two-dimensional domains

2023/04/17 by Raphaël Danchin, Danchin, Raphaël
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2304.08036

openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is devoted to the proof of time decay estimates for derivatives at any order of finite energy global solutions of the Navier-Stokes equations in general two-dimensional domains. These estimates only depend on the order of derivation and on the L2 norm of the initial data. The same elementary method just based on energy estimates and Ladyzhenskaya inequality also leads to Gevrey regularity results.

Related

• Decay of solutions to the three-dimensional generalized Navier-Stokes equations
• Regularity of solutions to the Navier-Stokes equations evolving from\n small data in BMO^-1
• Long time decay for global solutions to the Navier-Stokes equations in Sobolev-Gevery spaces
• Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations
• Infinite energy solutions of the two-dimensional Navier-Stokes equations