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arXiv · 1512.03116

Weak solutions for Euler systems with non-local interactions

José A. Carrillo·Eduard Feireisl·Piotr Gwiazda·Agnieszka Świerczewska-Gwiazda
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Abstract

We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the study of self-organisation in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of \emph{dissipative} solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction.

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José A. Carrillo, Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda. 2015-12-10. Weak solutions for Euler systems with non-local interactions. https://arxiv.org/abs/1512.03116

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