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 |
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Critical thresholds in 1D Euler equations with non-local forces
AU - Carrillo, José A.
AU - Choi, Young Pil
AU - Tadmor, Eitan
AU - Tan, Changhui
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84947039931&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84947039931&partnerID=8YFLogxK
U2 - 10.1142/S0218202516500068
DO - 10.1142/S0218202516500068
M3 - Article
AN - SCOPUS:84947039931
VL - 26
SP - 185
EP - 206
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 1
ER -