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The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. In convective (or Lagrangian) form it is written: where is the density at the point considered in the continuum (for which the continuity equation holds), is the stress tensor, and contains all of the body forces per unit mass (often simply gravitational acceleration). is the flow velocity vector field, which depends on time and space. where is the flux associated to the momentum density, and

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• Cauchy momentum equation
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• The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. In convective (or Lagrangian) form it is written: where is the density at the point considered in the continuum (for which the continuity equation holds), is the stress tensor, and contains all of the body forces per unit mass (often simply gravitational acceleration). is the flow velocity vector field, which depends on time and space. where is the flux associated to the momentum density, and
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• The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. In convective (or Lagrangian) form it is written: where is the density at the point considered in the continuum (for which the continuity equation holds), is the stress tensor, and contains all of the body forces per unit mass (often simply gravitational acceleration). is the flow velocity vector field, which depends on time and space. Notably, it can be written, through an appropriate change of variables, also in conservation (or Eulerian) form: where is the momentum density at the point considered in the continuum (for which the continuity equation holds), is the flux associated to the momentum density, and contains all of the body forces per unit volume.
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