Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
复制标题
DOI：
10.1016/j.aim.2011.05.005
复制
发表时间：
2010-07
影响因子：
1.7
通讯作者：
Philip T. Gressman;Robert M. Strain
中科院分区：
文献类型：
--
作者：
Philip T. Gressman;Robert M. Strain
本文给出了在三线性L2（Rn）能量< Q（g，f），f>下具有全范围物理非截断碰撞核（γ>− n和s∈（0，1））的Boltzmann碰撞算符的精确构造性上下界估计.这些新的估计证明了，对于一个非常一般的g（v）类，能量空间中的全局扩散行为（在f上）是我们早期工作中线性化背景下确定的几何分数导数半范数的行为（Gressman和Strain，2010 [15]，2011 [16]）。我们进一步证明了新的全局熵产生估计具有相同的各向异性半范数。这解决了长期以来，广泛的启发式猜想的尖锐的扩散性质的非截止玻尔兹曼碰撞算子在能量空间L2（Rn）。
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 L 2 (R n) 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 L 2 (R n).