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SP90
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Homework Statement
Homework Equations
So I have that [itex] v \otimes n = \left( \begin{array}{ccc}
v_{1}n_{1} & v_{1}n_{2} & v_{1}n_{3} \\
v_{2}n_{1} & v_{2}n_{2} & v_{2}n_{3} \\
v_{3}n_{1} & v_{3}n_{2} & v_{3}n_{3} \end{array} \right)
[/itex]
The Attempt at a Solution
I've tried applying the Divergence theorem for Tensors:
[itex]
\int_{\partial B} ( v \otimes n )n dA = \int_{B} \nabla \cdot ( v \otimes n ) dV
[/itex]
But that doesn't lead anywhere particularly useful. I thought it might be worth noting that [itex]\nabla \cdot ( v \otimes n ) = \frac{dv_{1}}{dx_{1}}n_{1}+\frac{dv_{2}}{dx_{2}}n_{2} + \frac{dv_{3}}{dx_{3}}n_{3}[/itex] but I can't seem to get anywhere near [itex]\nabla v[/itex]
And this problem isn't homework, it's just an optional exercise, but it's frustrated me for a while and I figured I should get some pointers.
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