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arXiv · 2606.16008

Equilibria of the Pressureless Euler System in Dimension 1

Nicholas Biglin·Joseph Crachiola·Thomas Kunz·Omkar Maralappanavar
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Abstract

The pressureless Euler equations in dimension 1 describe the evolution of a distribution of mass over the real line. We are interested in sticky particles solutions: distributional solutions in which mass that collides sticks together for all time. Given initial data, a projection formula is known to give a sticky particles solution. We obtain a necessary and sufficient condition for this solution to go to equilibrium based only on the initial condition. Furthermore, we give a precise characterization of the equilibrium, as well as a formula for the time of collapse.

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Nicholas Biglin, Joseph Crachiola, Thomas Kunz, Omkar Maralappanavar. 2026-06-14. Equilibria of the Pressureless Euler System in Dimension 1. https://arxiv.org/abs/2606.16008

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