The Boltzmann equation, Besov spaces, and optimal time decay rates in
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- 作者：Vedran Sohinger1 ; vedranso@math.upenn.edu" class="auth_mail ; Robert M. Strain2 ; strain@math.upenn.edu" class="auth_mail
- 关键词：35Q20 ; 35R11 ; 76P05 ; 82C40 ; 35B65 ; 26A33
- 刊名：Advances in Mathematics
- 出版年：20 August 2014
- 年：2014
- 卷：261
- 期：Complete
- 页码：274-332
- 全文大小：758 K
文摘
We prove that k -th order derivatives of perturbative classical solutions to the hard and soft potential Boltzmann equation (without the angular cut-off assumption) in the whole space, 
with n≥3, converge in large time to the global Maxwellian with the optimal decay rate of in the -norm for any 2≤r≤∞. These results hold for any 媳∈(0,n/2] as long as initially . In the hard potential case, we prove faster decay results in the sense that if and for edaa127baddcf7d" title="Click to view the MathML source">媳∈(n/2,(n+2)/2] then the solution decays the global Maxwellian in with the optimal large time decay rate of .
with n≥3, converge in large time to the global Maxwellian with the optimal decay rate of in the -norm for any 2≤r≤∞. These results hold for any 媳∈(0,n/2] as long as initially . In the hard potential case, we prove faster decay results in the sense that if and for edaa127baddcf7d" title="Click to view the MathML source">媳∈(n/2,(n+2)/2] then the solution decays the global Maxwellian in with the optimal large time decay rate of .