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arXiv · 1802.08926

Global existence and stability of nearly aligned flocks

Roman Shvydkoy
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Abstract

We study regularity of a hydrodynamic singular model of collective behavior introduced in \cite{ST1}. In this note we address the question of global well-posedness in multi-dimensional settings. It is shown that any initial data $(u,ρ)$ with small velocity variations $|u(x) - u(y)| < \e$ relative to its higher order norms, gives rise to a unique global regular solution which aligns and flocks exponentially fast. Moreover, we prove that the limiting flocks are stable.

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Roman Shvydkoy. 2018-03-14. Global existence and stability of nearly aligned flocks. https://doi.org/10.1007/s10884-018-9693-8

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