Correct differentiation identity? (tensors, vectors)

  • Thread starter Waldheri
  • Start date
Hello,

I'm working on some problems and I want to pose the following, though I am not completely sure it is correct. Can somebody point me to some sources on this? I have tried googling myself, but I only found differentiation identities with either just vectors and scalars on the on hand, or dot products between tensors on the other hand.

Note: [itex]\boldsymbol{A}[/itex] denotes a second-order tensor, [itex]\vec{v}[/itex] denotes a vector and [itex]:[/itex] the double dot product.

[tex]\nabla\cdot(\vec{v}\cdot\boldsymbol{A}) = \nabla\vec{v}:\boldsymbol{A} + \vec{v}\cdot\nabla\cdot\boldsymbol{A}[/tex]

So in other words: is the above identity correct?
 
Last edited by a moderator:

Want to reply to this thread?

"Correct differentiation identity? (tensors, vectors)" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top