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Mathematics > Analysis of PDEs

arXiv:1804.09340 (math)
[Submitted on 25 Apr 2018 (v1), last revised 3 Jul 2020 (this version, v7)]

Title:Sticky particles and the pressureless Euler equations in one spatial dimension

Authors:Ryan Hynd
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Abstract:We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they remain stuck together thereafter. Our main result is that if the interaction potential is semi-convex, this sticky particle property can quantified and is preserved upon letting the number of particles tend to infinity. This is used to show that solutions of the pressureless Euler equations exist for given initial conditions and satisfy an entropy inequality.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.09340 [math.AP]
  (or arXiv:1804.09340v7 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.09340

Submission history

From: Ryan Hynd [view email]
[v1] Wed, 25 Apr 2018 04:34:07 UTC (572 KB)
[v2] Mon, 14 May 2018 22:08:58 UTC (573 KB)
[v3] Wed, 24 Oct 2018 01:00:22 UTC (601 KB)
[v4] Fri, 26 Oct 2018 02:37:42 UTC (601 KB)
[v5] Fri, 28 Dec 2018 20:50:19 UTC (602 KB)
[v6] Fri, 27 Dec 2019 02:15:31 UTC (596 KB)
[v7] Fri, 3 Jul 2020 18:37:26 UTC (596 KB)
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