On product formulas for nonlinear semigroups

Abstract

We study a number of sufficient conditions which guarantee the convergence of semigroup product formulas of the type H_t = lim n∞(F_(t/n)^oG_(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.

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