The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity

In [C2], Chemin shows that solutions of the Navier-Stokes equations in R-2 for an incompressible fluid whose initial vorticity lies in L-2 boolean AND L-infinity 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. In [Y2], Yudovich assumes an initial vorticity lying in L-p for all p greater than or equal to p(0), and establishes the uniqueness of solutions to the Euler equations for an incompressible fluid in a bounded domain of R-n, 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 R-2, 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 p(0) = 2. The resulting bounded rate of convergence can be arbitrarily slow as a function of the viscosity nu.