Critical thresholds in 1D Euler equations with non-local forces
File(s)Critical_thesholds_1D_Euler_CCTT.pdf (336.97 KB)
Accepted version
Author(s)
Carrillo, JA
Choi, Y-P
Tadmor, E
Tan, C
Type
Journal Article
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.
Date Issued
2015-10-20
Date Acceptance
2015-08-11
Citation
Mathematical Models & Methods in Applied Sciences, 2015, 26 (1)
ISSN
1793-6314
Publisher
World Scientific Publishing
Journal / Book Title
Mathematical Models & Methods in Applied Sciences
Volume
26
Issue
1
Copyright Statement
Electronic version of an article published as Mathematical Models & Methods in Applied Sciences, Volume 26, 185 https://dx.doi.org/10.1142/S0218202516500068 © 2015 copyright World Scientific Publishing Company http://www.worldscientific.com/doi/10.1142/S0218202516500068
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Flocking
alignment
hydrodynamics
regularity
critical thresholds
POISSON EQUATIONS
GLOBAL REGULARITY
PARTICLE
SIMULATION
FLOCKING
SYSTEMS
LIMIT
FISH
Publication Status
Published
Article Number
185