Understanding the Laplacian Operator: ∇(∇ * q) vs. Other Operations

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SUMMARY

The discussion clarifies that the expression ∇(∇ * q) represents the gradient of the divergence of vector field q, which is equivalent to the Laplacian operator plus additional terms. Specifically, the additional terms include curl(curl(q)). This distinction is crucial for understanding vector calculus operations and their implications in various applications.

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  • Understanding of vector calculus concepts, particularly divergence and curl.
  • Familiarity with the Laplacian operator and its applications.
  • Knowledge of vector fields and their mathematical representations.
  • Basic proficiency in mathematical notation and operations involving the nabla operator (∇).
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franky2727
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∇(∇ * q) does this equal the laplacian or something else?
 
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I'm going to guess that's supposed to be a dot product on the first nabla? That makes it grad(div(q)). It's equal to the laplacian plus some other stuff. The other stuff is curl(curl(q)).
 

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