The global Cauchy problem for compressible Euler equations with a nonlocal dissipation
Analysis of PDEs
2018-01-16 v1
Abstract
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic Cucker-Smale flocking equation with strong local alignment forces and diffusions through the hydrodynamic limit based on the relative entropy argument. In a perturbation framework, we establish the global existence of a unique strong solution for the system under suitable smallness and regularity assumptions on the initial data. We also provide the large-time behavior of solutions showing the fluid density and the velocity converge to its averages exponentially fast as time goes to infinity.
Cite
@article{arxiv.1801.04683,
title = {The global Cauchy problem for compressible Euler equations with a nonlocal dissipation},
author = {Young-Pil Choi},
journal= {arXiv preprint arXiv:1801.04683},
year = {2018}
}