Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts

We study a two-dimensional coordinate-free model for the motion of flame fronts. The model specifies the normal velocity of the interface in terms of geometric information, such as the mean curvature and the Gaussian curvature of the front. As the tangential velocities do not determine the position of the interface, we choose them to maintain a favorable parameterization. We choose this to be an isothermal parameterization. After appropriately reformulating the equations of motion, we use the energy method to prove short-time well-posedness in Sobolev spaces.(c) 2023 Elsevier B.V. All rights reserved.