Strong trajectory and global \mathbfW^1,p-attractors for the damped-driven Euler system in \mathbb R²

2015/11/12 by Vladimir V. Chepyzhov, Chepyzhov, V. V., Alexei Ilyin +3
Engineering · Mathematics · #35B40 #35B41 #35Q35 #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.1511.03873

openalex publication_date 2015/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space H¹. A similar result on the strong attraction holds in the spaces H¹∩\u: ‖curl u‖_L^p

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