Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (6): 2131-2140.doi: 10.1016/S0252-9602(12)60165-9

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EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE

 WEI Jin-Bo, ZHANG Xian-Wen   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2011-07-18 Revised:2012-04-19 Online:2012-11-20 Published:2012-11-20
  • Supported by:

    The research was supported by the Fundamental Re-search Funds for the Central Universities (2012TS008) and the National Natural Science Foundation of China (11026054).

Abstract:

In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More pre-cisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp{−p|x v|2}, which has infinite mass and energy.

Key words: inelastic Boltzmann equation, infinite energy, external force

CLC Number: 

  • 82C40
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