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Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts
Journal article   Open access   Peer reviewed

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

Shunlian Liu and David M. Ambrose
Physica. D, v 447
May 2023
url
http://manuscript.elsevier.com/S0167278923000362/pdf/S0167278923000362.pdfView
Accepted (AM)Open Access (Publisher-Specific) Open

Abstract

Coordinate-free Energy method Flame front Free boundary problem Well-posedness
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. •We study a model for flame fronts introduced by Frankel and Sivashinsky.•The front is the two-dimensional boundary between three-dimensional gases.•We derive an evolutionary form of the model.•We prove well-posedness by the energy method.•The proof adapts ideas from numerical work of Hou, Lowengrub, and Shelley.

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Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Mathematics, Applied
Physics, Fluids & Plasmas
Physics, Mathematical
Physics, Multidisciplinary
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