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\frac{D {\bf u}}{Dt}  = \frac{1}{\rho} \nabla {\bf \sigma} + {\bf g}

where

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body( t, {\bf r} )

time and spatial variables

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body{\bf u}(t, {\bf r})

velocity of  Continuum Body 

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body\rho(t, {\bf r})

density of  Continuum Body 

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body\sigma(t, {\bf r})

stress tensor of Continuum Body 

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body{\bf g}(t, {\bf r})

sum of all body forces exerted on Continuum Body 

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body--uriencoded--%7B\bf f%7D_%7B\rm cnt%7D(t, %7B\bf r%7D)

volumetric density of all contact forces exerted on Continuum Body

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body--uriencoded--\frac%7BD%7D%7BDt%7D = \frac%7B\partial %7D%7B\partial t%7D + %7B\bf u%7D \nabla

Material derivative of the Continuum Body motion


In Fluid Mechanics it's known as Navier–Stokes equation and based on specific view of the stress tensor.

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\sigma = - p  - \mu \cdot \left[  \Delta {\bf u} + \frac{1}{3} {\bf u} \nabla {\bf u}  \right]


See also

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Physics / Mechanics / Continuum mechanics 

[  Continuum Body  ] [ Navier–Stokes equation ]