Abstract We prove that if a pair of Kähler classes is J -nef, the J -flow on a compact Kähler surface converges to a weak solution of the Monge-Ampère equation in the sense of currents. We also establish the same convergence behavior for the deformed Hermitian-Yang-Mills flow. The method is based on a property of a limit of viscosity subsolutions.
Rei Murakami (2026) studied this question.