AVERAGE REGULARITY OF THE SOLUTION TO AN EQUATION WITH THE RELATIVISTIC-FREE TRANSPORT OPERATOR

doi:10.1016/S0252-9602(17)30073-5

Abstract

Abstract:

Let u=u (t,x,p) satisfy the transport equation =f,where f=f (t,x,p) belongs to L^p ((0,T)×R³×R³) for 1 < p < ∞ and is the relativisticfree transport operator from the relativistic Boltzmann equation.We show the regularity of ∫_R³ u(t,x,p) dp using the same method as given by Golse,Lions,Perthame and Sentis.This average regularity is considered in terms of fractional Sobolev spaces and it is very useful for the study of the existence of the solution to the Cauchy problem on the relativistic Boltzmann equation.

Key words: regularity, transport operator, relativistic Boltzmann equation

Jianjun HUANG, Zhenglu JIANG. AVERAGE REGULARITY OF THE SOLUTION TO AN EQUATION WITH THE RELATIVISTIC-FREE TRANSPORT OPERATOR[J].Acta mathematica scientia,Series B, 2017, 37(5): 1281-1294.

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