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Mathematics > Analysis of PDEs

arXiv:1411.1791 (math)
[Submitted on 6 Nov 2014 (v1), last revised 24 May 2015 (this version, v2)]

Title:Critical thresholds in 1D Euler equations with nonlocal forces

Authors:José A. Carrillo, Young-Pil Choi, Eitan Tadmor, Changhui Tan
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Abstract:We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global in time existence or finite-time blow-up of strong solutions. When the interaction forces are considered, we also give a classification of the critical thresholds according to the different type of interaction forces. We also analyze conditions for global in time existence when the repulsion is modeled by the isothermal pressure law.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1411.1791 [math.AP]
  (or arXiv:1411.1791v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1411.1791

Submission history

From: Eitan Tadmor [view email]
[v1] Thu, 6 Nov 2014 23:05:20 UTC (17 KB)
[v2] Sun, 24 May 2015 04:21:36 UTC (17 KB)
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