Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production |
| |
Authors: | Philip T Gressman Robert M Strain |
| |
Institution: | University of Pennsylvania, Department of Mathematics, David Rittenhouse Lab., 209 South 33rd Street, Philadelphia, PA 19104-6395, USA |
| |
Abstract: | This article provides sharp constructive upper and lower bound estimates for the Boltzmann collision operator with the full range of physical non-cut-off collision kernels (γ>−n and s∈(0,1)) in the trilinear L2(Rn) energy 〈Q(g,f),f〉. These new estimates prove that, for a very general class of g(v), the global diffusive behavior (on f) in the energy space is that of the geometric fractional derivative semi-norm identified in the linearized context in our earlier works (Gressman and Strain, 2010 15], 2011 16]). We further prove new global entropy production estimates with the same anisotropic semi-norm. This resolves the longstanding, widespread heuristic conjecture about the sharp diffusive nature of the non-cut-off Boltzmann collision operator in the energy space L2(Rn). |
| |
Keywords: | MSC: 35Q20 35R11 76P05 82C40 35B65 26A33 |
本文献已被 ScienceDirect 等数据库收录! |
|