What Defines a Solenoidal Vector Field?

tweedle2
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Homework Statement
So I know how to work out if a vector field is incompressible normally, the divergence is 0. However I don't know how to do it for cylindrical or spherical coordinates, can anyone help me
Relevant Equations
Div f = 0
ac.PNG
 
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So is there some elegant way to do this or am I just supposed to follow my nose and sub the Taylor expansions for terms in the two boost matrices under the assumption ##v,w\ll 1##, then do three ugly matrix multiplications and get some horrifying kludge for ##R## and show that the product of ##R## and its transpose is the identity matrix with det(R)=1? Without loss of generality I made ##\mathbf{v}## point along the x-axis and since ##\mathbf{v}\cdot\mathbf{w} = 0## I set ##w_1 = 0## to...

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