Journal article
Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts
Physica. D, v 447
May 2023
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Abstract
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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Details
- Title
- Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts
- Creators
- Shunlian Liu (Corresponding Author) - Hunan University of TechnologyDavid M. Ambrose (Corresponding Author) - Drexel University
- Publication Details
- Physica. D, v 447
- Publisher
- Elsevier
- Grant note
- 12001187 / National Natural Science Foundation of China (http://dx.doi.org/10.13039/501100001809) 2020JJ5123 / Natural Science Foundation of Hunan Province of China DMS-1907684 / National Science Foundation, United States (http://dx.doi.org/10.13039/100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001001790100001
- Scopus ID
- 2-s2.0-85148689408
- Other Identifier
- 991020177852204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Fluids & Plasmas
- Physics, Mathematical
- Physics, Multidisciplinary