On product formulas for nonlinear semigroups

AbstractWe study a number of sufficient conditions which guarantee the convergence of semigroup product formulas of the type Ht=limn→∞(Ftn°Gtn)n and its generalizations. Our hypotheses differ from those of other authors in that we do not 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-Stokes equations