Weak and classical solutions of a family of second grade fluids

Abstract This paper shows that the decomposition method introduced by Cioranescu and Ouazar [Non-linear Partial Differential Equations 109, 178 (1984)] allows the proof of global existence in time of the weak solution of a class of second grade fluids in three dimensions with small data. It is also proven that this solution is a classical solution when the data are sufficiently smooth.