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I am programming viscous terms of compressible Navier-Stokes equations

U = {u[t, x, y, z], v[t, x, y, z], w[t, x, y, z]};
a = Div[\[Mu][x, y, z]*(Grad[U, {x, y, z}] + Transpose[Grad[U, {x, y, z}]]), {x, y, z}];

Now, I want to prevent Mathematica from expanding the product rule. In other words I want to have

a = {d/dx( ... ) + d/dy( ... ) + d/dz( ... ), 
d/dx( ... ) + d/dy( ... ) + d/dz( ... ), 
d/dx( ... ) + d/dy( ... ) + d/dz( ... )}

Can you help me out with that? Thanks in advance!

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  • $\begingroup$ use a new name e.g. "ddx" $\endgroup$ Sep 22 at 16:47

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You can use Inactive[Div] instead of Div. When you are ready to evaluate the differentiations, use the substitution /.Inactive[x_]->x.

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    $\begingroup$ You could also use Activate instead of a replacement rule to get rid of the Inactive wrappers $\endgroup$
    – Lukas Lang
    Sep 22 at 22:54

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