Short-time behaviour of a modified Laplacian coflow of G2-structures

We modify the Laplacian coflow of co-closed G2-structures - $\frac{d}{dt}\psi =\Delta \psi $ where $\psi $ is the closed dual 4-form of a $G_{2}$-structure $\varphi $. The modified flow is now parabolic in the direction of closed forms upto diffeomorphisms. We then prove short time existence and uniqueness of solutions to the modified flow.