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arXiv · 1804.07611

Regular solutions to the fractional Euler alignment system in the Besov spaces framework

Raphaël Danchin·Piotr B. Mucha·Jan Peszek·Bartosz Wróblewski
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Abstract

We here construct (large) local and small global-in-time regular unique solutions to the fractional Euler alignment system in the whole space ${\mathbb R}^d$, in the case where the deviation of the initial density from a constant is sufficiently small. Our analysis strongly relies on the use of Besov spaces of the type $L^1(0,T;\dot B^s_{p,1})$, which allow to get time independent estimates for the density even though it satisfies a transport equation with no damping. Our choice of a functional setting is not optimal but aims at providing a transparent and accessible argumentation.

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Raphaël Danchin, Piotr B. Mucha, Jan Peszek, Bartosz Wróblewski. 2018-04-20. Regular solutions to the fractional Euler alignment system in the Besov spaces framework. https://arxiv.org/abs/1804.07611

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