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arXiv · 0903.3226

Infinite-energy 2D statistical solutions to the equations of incompressible fluids

James P. Kelliher
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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.

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James P. Kelliher. 2009-03-18. Infinite-energy 2D statistical solutions to the equations of incompressible fluids. https://doi.org/10.1007/s10884-009-9151-8

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