Boltzmann equation: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
Carl McBride (talk | contribs) m (→References: Added a publication) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Stub-general}} | {{Stub-general}} | ||
The '''Boltzmann equation''' is given by ( | The '''Boltzmann equation''' is given by (<ref>[http://store.doverpublications.com/0486647412.html Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications]</ref> Eq 1 Chap. IX) | ||
:<math>\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cdot \frac{\partial f_i}{\partial {\mathbf u}_i } + \sum_j C(f_i,f_j) </math> | :<math>\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cdot \frac{\partial f_i}{\partial {\mathbf u}_i } + \sum_j C(f_i,f_j) </math> | ||
where <math></math> is an external force and the function C() represents binary collisions. | where <math></math> is an external force and the function C() represents binary collisions. | ||
==Solution== | |||
Recently Gressman and Strain <ref>[http://dx.doi.org/10.1073/pnas.1001185107 Philip T. Gressman and Robert M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions", Proceedings of the National Academy of Sciences of the United States of America '''107''' pp. 5744-5749 (2010)]</ref> have provided a proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation. | |||
==See also== | ==See also== | ||
*[[H-theorem]] | *[[H-theorem]] | ||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1007/s00222-004-0389-9 L. Desvillettes and Cédric Villani "On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation", Inventiones mathematicae '''159''' pp. 245-316 (2005)] | |||
[[category: non-equilibrium thermodynamics]] | [[category: non-equilibrium thermodynamics]] | ||
Latest revision as of 10:30, 20 June 2017
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
The Boltzmann equation is given by ([1] Eq 1 Chap. IX)
where is an external force and the function C() represents binary collisions.
Solution[edit]
Recently Gressman and Strain [2] have provided a proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation.
See also[edit]
References[edit]
- ↑ Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications
- ↑ Philip T. Gressman and Robert M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions", Proceedings of the National Academy of Sciences of the United States of America 107 pp. 5744-5749 (2010)
- Related reading