  Chemin has shown that solutions of the Navier-Stokes equations in the plane
for an incompressible fluid whose initial vorticity is bounded and lies in L^2
converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler
equations, convergence being uniform over any finite time interval. Yudovich,
assuming an initial vorticity lying in L^p for all p >= q for some q,
established the uniqueness of solutions to the Euler equations for an
incompressible fluid in a bounded domain of n-space assuming a particular bound
on the growth of the L^p-norm of the initial vorticity as p grows large. We
combine these two approaches to establish, in the plane, the uniqueness of
solutions to the Euler equations and the same zero-viscosity convergence as
Chemin, but under Yudovich's assumptions on the vorticity with q = 2. The
resulting bounded rate of convergence can be arbitrarily slow as a function of
the viscosity.
