Editing Classical field theory (section)

=== Continuum mechanics ===
==== Fluid dynamics ====
{{Main|Fluid dynamics}}

Fluid dynamics has fields of pressure, density, and flow rate that are connected by conservation laws for energy and momentum. The mass continuity equation is a continuity equation, representing the conservation of mass
<math display="block">\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf u) = 0 </math>
and the [[Navier–Stokes equations]] represent the conservation of momentum in the fluid, found from Newton's laws applied to the fluid,
<math display="block">\frac {\partial}{\partial t} (\rho \mathbf u) + \nabla \cdot (\rho \mathbf u \otimes \mathbf u + p \mathbf I) = \nabla \cdot \boldsymbol \tau + \rho \mathbf b </math>
if the density {{mvar|ρ}}, pressure {{mvar|p}}, [[deviatoric stress tensor]] {{mvar|'''τ'''}} of the fluid, as well as external body forces '''b''', are all given. The [[velocity field]] '''u''' is the vector field to solve for.