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arXiv · 0902.0706

Numerical studies on the self-similar collapse of the alpha-patches problem

Ana M. Mancho
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Abstract

This paper studies the dynamical evolution of the alpha-patches problem expressed in self-similar variables. A numerical algorithm is proposed and these equations are numerically explored. Several benchmarks of the code are discussed throughout the paper. Exact self-similar solutions are described and are found to play a role in separating collapsing from non-collapsing initial data: small perturbations around this solution blow up while others do not. Numerical simulations performed near convergent rescaled profiles, such as those described by Cordoba et al. in [12], indicate the absence of a stationary graph in the neighborhood of the rescaled profiles and suggest a more complex scenario for blow up.

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Ana M. Mancho. 2009-02-04. Numerical studies on the self-similar collapse of the alpha-patches problem. https://doi.org/10.1016/j.cnsns.2015.02.009

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