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Infinite Energy Solutions for Dissipative Euler Equations in R-2
Journal article   Open access   Peer reviewed

Infinite Energy Solutions for Dissipative Euler Equations in R-2

V Chepyzhov and S Zelik
Journal of Mathematical Fluid Mechanics, Vol.17(3), pp.513-532
29/06/2015

Abstract

Science & Technology Physical Sciences Technology Mathematics Interdisciplinary Applications Mechanics Physics Fluids & Plasmas Mathematics Physics Euler equations Ekman damping infinite energy solutions weighted energy estimates unbounded domains NAVIER-STOKES EQUATIONS SPATIALLY NONDECAYING SOLUTIONS UNBOUNDED-DOMAINS DIFFERENTIAL-EQUATIONS TRAJECTORY ATTRACTORS DIFFUSION SYSTEMS SPACES TIME
We study the system of 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.
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