关于Caflisch的一个不等式

Caflisch1，2]在Euler方程存在光滑解的假设下，证明了Boltzmann方程存在一个解，且该解在平均自由程趋于零的极限下与Euler解一致．不幸的是Caflisch的证明有错误，其关键的引理6．1的结论太弱，不足以完成主要定理的证明．事实上，Caflisch在证明主要定理时，使用了比引理6．1更强的结论，但并未说明．本文改进了Caflisch的一个重要不等式；加强了原引理6．1的结论，并在修正了原主要定理证明过程中的其它错误后完成了它的证明．

ON A CAFLISCH'S INEQUALITY

There are errata in Caflisch's paper on the relation between the nonlinearBoltzmann equation and the fluid dynamics, where the result of Lemma 6.1 is too weak tocomplete the proof of his main theorem. An inequality is now given, which is an improvementon a Caflisch's key inequality. By using this improved result, the result of Caflisch's Lemma6.1 is strengthened. In the course of correcting other errata in Caflisch's paper, the proof ofCaflisch's main theorem is completed.