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

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

Research output: Contribution to journalArticle

30 Citations (Scopus)

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 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
Volume26
Issue number1
DOIs
Publication statusPublished - 2016 Jan 1

Fingerprint

Critical Threshold
Euler equations
Euler Equations
Interaction
Compressible Euler Equations
Finite Time Blow-up
Dichotomy
Strong Solution
One Dimension
Pairwise
Alignment

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

Carrillo, José A. ; Choi, Young Pil ; Tadmor, Eitan ; Tan, Changhui. / Critical thresholds in 1D Euler equations with non-local forces. In: Mathematical Models and Methods in Applied Sciences. 2016 ; Vol. 26, No. 1. pp. 185-206.
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Critical thresholds in 1D Euler equations with non-local forces. / Carrillo, José A.; Choi, Young Pil; Tadmor, Eitan; Tan, Changhui.

In: Mathematical Models and Methods in Applied Sciences, Vol. 26, No. 1, 01.01.2016, p. 185-206.

Research output: Contribution to journalArticle

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