Convergence of the vanishing viscosity approximation for superpositions
of confined eddies
H.J. Nussenzveig Lopes, M. Lopes Filho, Yuxi Zheng
A confined eddy is a circularly symmetric flow with vorticity of compact
support and zero net circulation. Confined eddies with disjoint supports
can be superimposed to generate stationary weak solutions of the
two-dimensional incompressible inviscid Euler equations.
In this work, we consider the unique weak solution of the two-dimensional
incompressible Navier-Stokes equations having a disjoint superposition
of very singular confined eddies as the initial datum.
We prove the convergence of these weak solutions back to the initial
configuration, as the Reynolds number goes to infinity. This implies
that the stationary superposition of confined eddies with disjoint supports
is the unique physically correct weak solution of the two-dimensional
incompressible Euler equations.