Abstract: Abstract We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space $B^{1,p}_{2}(M, {\varLambda }^{2})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Λ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:math> for p > 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson ( Asian J. Math. 3 , 1–16 1999). For a detailed exposition see Krom and Salamon ( J. Symplectic Geom. 17 , 381–417 2019).