Regularity of finite-dimensional realizations for evolution equations

We show that a continuous local semiflow of Ck-maps on a finite-dimensional Ck-manifold M with boundary is in fact a local Ck-semiflow on M and can be embedded into a local Ck-flow around interior points of M under some weak assumption. This result is applied to an open regularity problem for finite-dimensional realizations of stochastic interest rate models.