Entropy Dissipation and Long-Range Interactions
Entropy Dissipation and Long-Range Interactions
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DOI：
10.1007/s002050000083
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发表时间：
2000-06
影响因子：
2.5
通讯作者：
Radjesvarane Alexandre;L. Desvillettes;C. Villani;B. Wennberg
中科院分区：
文献类型：
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作者：
Radjesvarane Alexandre;L. Desvillettes;C. Villani;B. Wennberg
我们研究了长程相互作用的玻耳兹曼碰撞算符，即没有Grad角截止假设。我们建立了一个泛函不等式，证明了在精确意义上，熵耗散控制着分布函数的光滑性。我们的估计是最优的，并且给出了线性和非线性情况的统一处理。我们还给出了几个分散在前人工作中的有用结果的简单而完备的证明。作为应用，我们得到了等离子体物理中柯西问题和朗道近似的几个有用的估计。
We study Boltzmann's collision operator for long-range interactions, i.e., without Grad's angular cut-off assumption. We establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function, in a precise sense. Our estimate is optimal, and gives a unified treatment of both the linear and the nonlinear cases. We also give simple and self-contained proofs of several useful results that were scattered in previous works. As an application, we obtain several helpful estimates for the Cauchy problem, and for the Landau approximation in plasma physics.