数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1262-1284.doi: S0252-9602(16)30068-6

• 论文 • 上一篇    下一篇

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

金春银   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2015-11-24 修回日期:2016-04-11 出版日期:2016-10-25 发布日期:2016-10-25
  • 作者简介:Chunyin JIN,jinchunyin@amss.ac.cn

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

Chunyin JIN   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2015-11-24 Revised:2016-04-11 Online:2016-10-25 Published:2016-10-25

摘要:

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system.

关键词: pressureless Euler system, Cucker-Smale model, entropy solution, flocking

Abstract:

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system.

Key words: pressureless Euler system, Cucker-Smale model, entropy solution, flocking

中图分类号: 

  • 35A15