Critical thresholds in 1D Euler equations with non-local forces

José A. Carrillo, Young Pil Choi, Eitan Tadmor, Changhui Tan

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)


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 blowup 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 remark on global-in-time existence when the repulsion is modeled by the isothermal pressure law.

Original languageEnglish
Pages (from-to)185-206
Number of pages22
JournalMathematical Models and Methods in Applied Sciences
Issue number1
Publication statusPublished - 2016 Jan 1

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics


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