Infinite energy solutions for Dissipative Euler equations in R^2

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.

arXiv admin note: text overlap with arXiv:1203.5733

References in corpus (4)

• Euler Equations of Incompressible Ideal Fluids
• Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations
• Infinite Energy Solutions for Damped Navier-Stokes Equations in R2
• Uniform boundedness and long-time asymptotics for the two-dimensional Navier-Stokes equations in an infinite cylinder

Cited by in corpus (1)

• Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions