Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (5): 1262-1284.doi: S0252-9602(16)30068-6

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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

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

CLC Number: 

  • 35A15
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