Moment inequalities for the boltzmann equation and applications to spatially homogeneous problems
Moment inequalities for the boltzmann equation and applications to spatially homogeneous problems
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DOI：
10.1007/bf02732431
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发表时间：
1997-09
影响因子：
1.6
通讯作者：
A. Bobylev
中科院分区：
文献类型：
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作者：
A. Bobylev
证明了Boltzmann碰撞积分的一些不等式。这些不等式可以看作是著名的Povzner不等式的推广。的不等式是用来获得估计的时刻的解决方案的空间均匀玻尔兹曼方程的广泛的一类分子间的力量。我们得到简单的必要和充分条件（潜在的）一致有界的所有时刻。对于具有紧支撑的势，证明了以下陈述：如果初始分布函数的所有矩都被Maxwell Aexp（− Bv 2）的相应矩所约束，则对于任何t> 0，解的所有矩都被另一个Maxwell A1 exp [−B1（t）v2]的相应矩所约束;对于硬球，B（t）= const。还获得了碰撞频率的估计。
Some inequalities for the Boltzmann collision integral are proved. These inequalities can be considered as a generalization of the well-known Povzner inequality. The inequalities are used to obtain estimates of moments of the solution to the spatially homogeneous Boltzmann equation for a wide class of intermolecular forces. We obtain simple necessary and sufficient conditions (on the potential) for the uniform boundedness of all moments. For potentials with compact support the following statement is proved: if all moments of the initial distribution function are bounded by the corresponding moments of the MaxwellianAexp(−Bv2), then all moments of the solution are bounded by the corresponding moments of the other MaxwellianA1exp[−B1(t)v2] for anyt> 0; moreoverB(t) = const for hard spheres. An estimate for a collision frequency is also obtained.