Divergence of a tensor vector product

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SUMMARY

The divergence of a tensor vector product, specifically expressed as ∇.(ŦK.𝓫), cannot be directly computed in the same manner as scalar and vector products. The established expansion for scalar and vector products is ∇.(a𝓫) = a∇.𝓫 + 𝓫.∇a. However, for tensors, the divergence is only applicable to one of the indices, represented as ∂iKibj, indicating a limitation in the generalization of divergence for tensor products.

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desmal
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can anybody tell me the expansion for the divergence of tensor vector product
\nabla.(\tilde{K}.\vec{b})
for the case of scalar and vector the expansion is given by
\nabla.(a\vec{b})=a\nabla.\vec{b}+\vec{b}.\nabla a
 
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hi desmal! :smile:

you can't have a divergence of a tensor

(well ok, you can have a vector-valued divergence, but only wrt one of the indices: ∂iKibj)
 

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