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arXiv · 2010.00737

Well-posedness and asymptotics of a coordinate-free model of flame fronts

David M. Ambrose·Fazel Hadadifard·J. Douglas Wright
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Abstract

We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter $\alpha$ which relates to how unstable the front might be. We first prove short-time well-posedness of the coordinate-free model, for any value of $\alpha>0.$ We then argue that near the threshold $\alpha \approx 1,$ the solution stays arbitrarily close to the solution of the weakly nonlinear Kuramoto--Sivashinsky (KS) equation, as long as the initial values are close.

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David M. Ambrose, Fazel Hadadifard, J. Douglas Wright. 2020-10-02. Well-posedness and asymptotics of a coordinate-free model of flame fronts. https://arxiv.org/abs/2010.00737

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