Stability of the generalized Lagrangian mean curvature flow in cotangent bundle

In this paper, we consider the stability of the generalized Lagrangian mean curvature flow of graph case in the cotangent bundle, which is first defined by Smoczyk-Tsui-Wang. By new estimates of derivatives along the flow, we weaken the initial condition and remove the positive curvature condition in Smoczyk-Tsui-Wang's work. More precisely, we prove that if the graph induced by a closed $1$-form is a special Lagrangian submanifold in the cotangent bundle of a Riemannian manifold, then the generalized Lagrangian mean curvature flow is stable near it.