Infinite energy solutions for Dissipative Euler equations in R^2

TL;DR

This paper investigates the global behavior of weak solutions to 2D Euler equations with Ekman damping, establishing well-posedness, dissipativity, and the existence of a global attractor in infinite energy spaces.

Contribution

It develops a weighted energy theory for Euler equations with damping and proves the existence of a weak global attractor in uniformly local spaces.

Findings

Global well-posedness of weak solutions established.

Dissipativity of solutions demonstrated.

Existence of a weak global attractor proved.

Abstract

We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the further development of the weighted energy theory for the Navier-Stokes and Euler type problems. In addition, the existence of weak locally compact global attractor is proved and some extra compactness of this attractor is obtained.