On product formulas for nonlinear semigroups

Marsden, J. E.

J. Funct. Anal., 13, (1973), 51-72


We study a number of sufficient conditions which guarantee the convergence of semigroup product formulas of the type

Ht = $\displaystyle \lim_{{n \to \infty}}^{}$(Ft/noGt/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.