Critical thresholds in 1D Euler equations with nonlocal forces
By José Antonio Carrillo, Young-Pil Choi, Eitan Tadmor, Changhui Tan. 2014
139 citations recorded by the source corpus.
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 blow-up 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 analyze conditions for global in time existence when the repulsion is modeled by the isothermal pressure law.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/616b0f4acbc686692d8a5c0e57b774641f50706e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Roman Shvydkoy
- Eitan Tadmor
- Mark H. Carpenter
- Travis C. Fisher
- Alexander Kurganov
- Vlad Vicol
- T. Buckmaster
In Computational Mechanics
- Roman Shvydkoy
- Eitan Tadmor
- Travis C. Fisher
- Mark H. Carpenter
- Alexander Kurganov
- Praveen Chandrashekar
- Vlad Vicol
- T. Buckmaster
Citations in the corpus
- Eulerian dynamics with a commutator forcing III. Fractional diffusion of order 0 (2017, methodology): “Starting with the seminal work of Cucker and Smale paper [4] and the follow-up works [7, 6, 10, 17, 2, 15] and reference therein, it has become clear that in order to achieve unconditional flocking in either the agent-based or the macroscopic descriptions (1.”