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

, Chemin shows that solutions of the Navier-Stokes equations in R 2 for an incompressible fluid whose initial vorticity lies in L 2 L 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 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 .