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 language | English |
|---|---|
| Pages (from-to) | 185-206 |
| Number of pages | 22 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2016 Jan 1 |
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics
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Cite this
Carrillo, J. A., Choi, Y. P., Tadmor, E., & Tan, C. (2016). Critical thresholds in 1D Euler equations with non-local forces. Mathematical Models and Methods in Applied Sciences, 26(1), 185-206. https://doi.org/10.1142/S0218202516500068