Talk:Helmholtz decomposition

message: Suggestions:  
1)To make the introduction a bit gentler,  I suggest moving the equation,
:\mathbf{F} = -\nabla \varphi + \nabla \times \mathbf{A}
to the beginning of the presentation.
:I agree Berland 13:18, 18 January 2007 (UTC)
replies: text: The more precise statement can in fact be seen from the Hodge decomposition (which this article refers to as a generalisation). Fast decay seems to be introduced here in order to eliminate the null-space of the Laplacian. This article lacks rigour as it does not state that it only considers vector fields on R^3 (in the first part at least). The section on the weak form repairs this. Bas Michielsen (talk) 23:51, 8 May 2008 (UTC)
thread_title: Suggestions

message: What is a rapidly decaying vector field ?  —Preceding unsigned comment added by 193.157.197.135 (talk) 12:01, 28 February 2011 (UTC)
thread_title:  Rapidly decaying vector field 

message: Excellent article! Just split some lines in the final section so that we're not equating scalar fields with vector fields. Even if both are zero, they are the zeros of different spaces...  — Preceding unsigned comment added by Sukarsono (talk • contribs) 16:58, 4 April 2011 (UTC)
replies: text: It's undoubtedly more rigorous to tell two zeroes apart, but you may regard writing the same as an abuse of notation. Could you imagine a situation where the difference between two zeroes will actually matter, say, affect the result of calculations or validity of a theorem? --Netheril96 (talk) 01:11, 5 April 2011 (UTC)
thread_title:  Clarified final section slightly 

message: This decomposition also seems to be called the Helmholtz–Weyl decomposition or even just the Weyl decomposition, and is a special case of the de Rham-Hodge-Kodaira decomposition on manifolds.
Probably the alternate names & generalizations should be mentioned in the lede.  Googling these terms uncovers many, many references, so it is only a matter of selecting the appropriate ones.
— Steven G. Johnson (talk) 18:36, 16 July 2013 (UTC)
thread_title:  Also called Helmholtz–Weyl decomposition 

message: It's not clear that the Helmholtz decomposition works by splitting into an operation on a scalar field and an operation on a vector field.  It is worded as "This implies" rather than stated, or explained why.  — Preceding unsigned comment added by 45.49.18.32 (talk) 21:55, 31 May 2015 (UTC)
replies: text: Better now?  Sławomir Biały (talk) 22:55, 31 May 2015 (UTC)
thread_title:  Intro needs work 

message: I think that "Helmholtz Decomposition Theorem" would be more appropriated for the title because in many places it is referred to the "Helmholtz Theorem" or the "Helmholtz Theorem of electromagnetism" etc. 
Best regards. Physicist137 (talk) 21:27, 29 April 2020 (UTC)
thread_title:  What do you think of changing the title by "Helmholtz Decomposition Theorem"? 

message: The formula for \Phi and A in the first section involve surface integrals. But these integrals are obviously null because F, being continuous and null outside V, should be null at the boundary of V. This is misleading. And if these surface integrals are removed, V can be replaced by \mathbb R^3, which is better
Thus, after proving the result with the help of a finite domain V, the proof can be extended to all functions that decay at least as fast as 1/r, by just multiplying F by a function that is equal to 1 on the ball of radius R, to 0 outside the ball of radius R+1, and sufficiently smooth in between.  That's just Lebesgue convergence formula. 
.maimonid (talk) 21:57, 7 May 2022 (UTC)
thread_title: Misleading formulae