Closed warped G2-structures evolving under the Laplacian flow

We study the behaviour of the Laplacian flow evolving closed G2-structures on warped products of the form M^6×S^1, where the base M^6 is a compact 6-manifold endowed with an SU(3)-structure. In the general case, we reinterpret the flow as a set of evolution equations on M^6 for the differential forms defining the SU(3)-structure and the warping function. When the latter is constant, we find sufficient conditions for the existence of solutions of the corresponding coupled flow. This provides a method to construct immortal solutions of the Laplacian flow on the product manifolds M^6×S^1. The application of our results to explicit cases allows us to obtain new examples of expanding Laplacian solitons.