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.
|Number of pages||22|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2016 Jan 1|
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics