共 32 条
On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: Averaging compactness of weak solutions
被引:9
|作者:
Lu, Xuguang
[1
]
机构:
[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China
基金:
中国国家自然科学基金;
关键词:
Boltzmann equation;
Fermi-Dirac particles;
coulomb interaction;
weak angular cutoff;
averaging compactness;
D O I:
10.1007/s10955-006-9039-5
中图分类号:
O4 [物理学];
学科分类号:
0702 ;
摘要:
The paper considers macroscopic behavior of a Fermi - Dirac particle system. We prove the L-1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi - Dirac particles in a periodic box with the collision kernel b(cos theta)| v - v*|(gamma), which corresponds to very soft potentials: - 5 < gamma <= - 3 with a weak angular cutoff: integral(pi)(0) b(cos theta) sin(3) theta d theta < infinity. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff - Young inequality, the L-infinity-bounds of the solutions, and a specific property of the value-range of the exponent gamma. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy.
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页码:517 / 547
页数:31
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