Existence of martingale solutions for stochastic flocking models with local alignment

Arnaud Debussche; Angelo Rosello

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arXiv · 2007.01512

Existence of martingale solutions for stochastic flocking models with local alignment

Arnaud Debussche·Angelo Rosello

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Abstract

We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor models. By regularizing the coefficients, we first construct approximate solutions obtained as the mean-field limit of the corresponding particle systems. We then establish the compactness in law of this family of solutions by relying on a stochastic averaging lemma. This extends the results obtained by Karper, Mellet and Trivisa in the deterministic case.

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Arnaud Debussche, Angelo Rosello. 2020-07-03. Existence of martingale solutions for stochastic flocking models with local alignment. https://arxiv.org/abs/2007.01512

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