期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 107, 期 13, 页码 5744-5749出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1001185107
关键词
kinetic theory; non cut-off; anisotropy; fractional derivatives
资金
- National Science Foundation [DMS-0850791, DMS-0901463]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0901463] Funding Source: National Science Foundation
This is a brief announcement of our recent proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation without any angular cutoff, that is, for long-range interactions. We consider perturbations of the Maxwellian equilibrium states and include the physical cross-sections arising from an inverse-power intermolecular potential r(-(p-1)) with p > 2, and more generally. We present here a mathematical framework for unique global in time solutions for all of these potentials. We consider it remarkable that this equation, derived by Boltzmann (1) in 1872 and Maxwell (2) in 1867, grants a basic example where a range of geometric fractional derivatives occur in a physical model of the natural world. Our methods provide a new understanding of the effects due to grazing collisions.
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