H. Brezis, GLOBAL-SOLUTIONS OF 2-DIMENSIONAL NAVIER-STOKES AND EULER EQUATIONS -REMARKS, Archive for Rational Mechanics and Analysis, 128(4), 1994, pp. 359-360
In the preceding paper, M. BEN-ARTZI establishes an interesting existe
nce and uniqueness result for the two-dimensional Navier-Stokes equati
on with initial vorticity in L1. The purpose of this note is to show t
hat one technical assumption ((1.19) in his notation) is not necessary
for uniqueness. We follow the same notation as in the preceding paper
.