Talk:Boltzmann equation

message: There is a confusion, very  common, between Liouville and Boltzman. The Liouville Equation is a N-particle equation whereas the Boltzmann Equation is a 1-Particle Equation. The Boltzman Equation is an approximation.   —Preceding unsigned comment added by Lionel sittler (talk • contribs) 13:28, 15 October 2007 (UTC)
thread_title:  Confusion

message: This page has no real description of the equation, lacks a good explanation of how it is used, and is otherwise in need of improvement.  FrozenPurpleCube 16:19, 17 April 2007 (UTC)
thread_title:  Technical 

message: Vlasov equation is completely different than Boltzman equation. The redirect should be detached. Temur (talk) 07:29, 14 January 2008 (UTC)
thread_title: Vlasov equation is different

message: Nowhere is it specified what the function g(p-p', q) is. Is it a Green's function? Could someone in the know correct this? 220.101.95.103 (talk) 06:54, 4 February 2010 (UTC)
thread_title:  Molecular chaos and the collision term 

message: This article has numerous problems basically everywhere (and I haven’t the patience to list them all out in excruciating detail like I usually do). A rewrite is in order - I'll do it soon. F = q(E+v×B) ⇄ ∑ici 10:30, 28 May 2012 (UTC)
thread_title:  Problems and rewrite 

message: In what respect is the so-called "stronger form" stronger? Usually when this term is used, the weaker form and stronger forms are NOT equivalent, they will apply in different circumstances. But it seems to me that the "stronger form" is exactly equivalent to the weaker form, just written out in a more explicit way. Can someone please clarify? Thanks, --Steve (talk) 16:58, 7 December 2012 (UTC)
replies: text: No clue. I changed to "General equation (principal form)" to "Principal statement" and "General equation (stronger form)" to "Final statement". Any better? Probably not, but not sure how else to re-title. No source as far as I can see even infers a "strong form". M∧Ŝc2ħεИτlk 14:36, 7 April 2013 (UTC)
thread_title:  "Stronger form" 

message: I'm fairly certain that the quantity "g" in the collision integral is always the relative velocity, and never the relative momentum, even for the case of a mixture. For one, the collision term does not have the proper units if "g" is a momentum. Secondly, in a two-body collision, the relevant quantities are center of mass momentum and relative velocity, not relative momentum. 70.124.92.52 (talk) 17:36, 25 June 2014 (UTC)
thread_title:  Relative momentum problem 

message: The equation is a nonlinear integro-differential equation (it was erroneously called linear stochastic PDE, now it is corrected). See, for example the modern textbook "...solving Boltzmann's equation will be an arduous task since it is both nonlinear and has an integro-differential form..." (page 69 of Harris S. An introduction to the theory of the Boltzmann equation. Courier Corporation; 2004.)Agor153 (talk) 12:56, 16 April 2016 (UTC)
thread_title:  The Boltzmann equation is a [[Nonlinear system|nonlinear]] [[integro-differential equation]],  

message: Someone has written "Until this breakthrough in analytical solution approaches, the various forms of the Boltzmann equation were solved using numerical methods". I have the feeling that the past tense alongside the word "until" imply that we have analytical solutions for the general Boltzmann equation on arbitrary initial distributions, so that numerics in this field are completely obsolete. I can't find a hint about this in the cited paper. I would suggest that someone gives a reference for at least one Boltzmann solver that actually calculates or at least uses the analytical solution, otherwise the first part of this sentence should be deleted and the tense should be adjusted.
And sorry if my potential lack of knowledge about this language created a misunderstanding.  141.24.116.106 (talk) 16:38, 1 June 2016 (UTC)
replies: text: I agree 100%. I edited according to your suggestion just now. --Steve (talk) 14:37, 21 February 2018 (UTC)
thread_title:  Solution of the Boltzmann equation  

message: Can someone fix these equations? Beowulf (talk) 13:10, 4 April 2018 (UTC)
replies: text: Are you sure? They all look fine on my computer, unless I'm missing something. Try reloading the page maybe? --Steve (talk) 16:14, 4 April 2018 (UTC)
thread_title:  Mathematical equations do not parse 

message: The principal statement has the three terms  (force, diff, and coll) and then says that 'Expressions for each term on the right side are provided below.'
The final statement still has the collision term, but the force and diffusive terms are now replaced by three terms on the left of the final statement. Is there a way to connect this equation back to the principal statement, by stating which parts of the final statement refer to force term and which parts of the final statement refer to the diffusive term? Alamo NM (talk) 19:26, 10 September 2021 (UTC)
thread_title:  Comparison of 'Principal statement' to 'Final statement' 

message: In section "General equation (for a mixture)" the collision integral should be written:
\left(\frac{\partial f_i}{\partial t} \right)_{\mathrm{coll}} = \sum_{j=1}^n \iint g_{ij} I_{ij}(g_{ij}, \Omega)[f'_i f'_j - f_if_j] \,d\Omega\,d^3\mathbf{p'_i},
 Concave Hull (talk) 23:15, 16 January 2022 (UTC)
thread_title:  Missing i in integral equation