GLOBAL-SOLUTIONS OF 2-DIMENSIONAL NAVIER-STOKES AND EULER EQUATIONS

Long-time solutions to the Navier-Stokes (NS) and Euler (E) equations of incompressible flow in the whole plane are constructed, under the assumption that the initial vorticity is in L1 (R2) for (NS) and in L1 (R2) and L(r) (R2) for some r > 2 for (E). It is shown that the solution to (NS) is unique, smooth and depends continuously on the initial data, and that the (velocity) solution to (E) is Holder continuous in the space and time coordinates. It is shown that as the viscosity vanishes, there is a subsequence of solutions to (NS) converging to a solution of (E).