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    \mathbf{P} and \mathbf{Q} are both vector fields. Somewhere in the question I have the expression: \mathbf{Q} \cdot \nabla ^2 \mathbf{P}

    What does the \nabla ^2 mean here?

    Any help would be appreciated. Thanks
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    It's the Laplacian operator which has different meanings depending on what co-ordinate system you're dealing with.

    What you've written makes no sense anyway becuase the result of the Laplacian is a scalar quantity and you need two vectors for a dot product.

    Forget that , it does make sense when you have it as an operator acting on Q as others have pointed out.
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    Where as \nabla usually denotes \dfrac{\partial}{\partial x_i}, \nabla^2 usually denotes \dfrac{\partial^2}{\partial x_i \partial x_i} (with summation convention).
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    (Original post by lilman91)
    \mathbf{P} and \mathbf{Q} are both vector fields. Somewhere in the question I have the expression: \mathbf{Q} \cdot \nabla ^2 \mathbf{P}

    What does the \nabla ^2 mean here?

    Any help would be appreciated. Thanks
    If you are in cartesian coordinates it means the lapacian applied to each component of P so in this case you have Q.(grad^2(Pi)) where Pi is the ith component of P.

    In non Cartesian coordinates it is defined by this identity (which still holds in cartesian)

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    (Original post by thebadgeroverlord)
    If you are in cartesian coordinates it means the lapacian applied to each component of P so in this case you have Q.(grad^2(Pi)) where Pi is the ith component of P.

    In non Cartesian coordinates it is defined by this identity (which still holds in cartesian)

    Cheers. So would this be the right notation in summation convention:

    \mathbf{Q} \cdot \nabla ^2\mathbf{P} = Q_j \frac{\partial^2}{\partial x_i \partial x_i}P_j
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    (Original post by lilman91)
    Cheers. So would this be the right notation in summation convention:

    \mathbf{Q} \cdot \nabla ^2\mathbf{P} = Q_j \frac{\partial^2}{\partial x_i \partial x_i}P_j
    Yes
 
 
 
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