The Donaldson geometric flow is a local smooth semiflow

Abstract

We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space $B_2^{1,p}(M,{\Lambda }^2)$ for $p>4$. The Donaldson geometric flow was introduced by Simon Donaldson in [2]. For a detailed exposition see [6].