Journal of Dynamics and Differential Equations

, 21:631

Infinite-Energy 2D Statistical Solutions to the Equations of Incompressible Fluids

Authors

    • Department of MathematicsUniversity of California
Open AccessArticle

DOI: 10.1007/s10884-009-9151-8

Cite this article as:
Kelliher, J.P. J Dyn Diff Equat (2009) 21: 631. doi:10.1007/s10884-009-9151-8

Abstract

We develop the concept of an infinite-energy statistical solution to the Navier–Stokes and Euler equations in the whole plane. We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity, which includes the important special case of vortex patch initial data. Our approach is to use well-studied properties of statistical solutions in a ball of radius R to construct, in the limit as R goes to infinity, an infinite-energy solution to the Navier–Stokes equations. We then construct an infinite-energy statistical solution to the Euler equations by making a vanishing viscosity argument.

Keywords

Statistical solutions Navier–Stokes equations Euler equations

Mathematics Subject Classification (2000)

76D06 76D05

Copyright information

© The Author(s) 2009