I recently came across the vector version of the Navier Stokes equations for fluid flow.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\displaystyle{\frac{\partial \mathbf{u}}{\partial \mathbf{t}}} + ( \mathbf{u} \cdot \bigtriangledown) \mathbf{u} = v \bigtriangleup \mathbf{u} - grad \ p[/tex]

Ok, all is well until [tex]\bigtriangleup[/tex]. I know this represents the laplacian. What is the formulation of the Laplacian for this since it is a vector? Is it just simply the second partials dot product with the respective terms of the vector? Or is it something else?

edit: changed text where I say problem is [tex] \bigtriangledown[/tex] to the appropriate [tex]\bigtriangleup[/tex]

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# Navier Stokes Equation

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