Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel

Debora Amadori; Cleopatra Christoforou

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arXiv · 2309.01939

Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel

Debora Amadori·Cleopatra Christoforou

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Abstract

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in [2] to the Cauchy problem for any $BV$ initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.

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Debora Amadori, Cleopatra Christoforou. 2023-09-05. Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel. https://arxiv.org/abs/2309.01939

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