**Marsden, J. E.
**

We study a number of sufficient conditions which guarantee the convergence of semigroup product formulas of the type
*H*_{t} = (*F*_{t/n}`o`*G*_{t/n})^{n}

and its generalizations. Our hypotheses differ from those of other authors in that we do no assume in advance that the limit operator is a generator. Rather this is a consequence and hence the above formula yields an existence theorem (local in time) for nonlinear semigroups. A number of smoothness properties are studied as well. The results may be applied to and are motivated by the Navier-Stroke equations.