===== Navier–Stokes equations =====
==== Set ====

| @#55CCEE: context     | @#55CCEE: $ n\in\mathbb N $ |
| @#55CCEE: context     | @#55CCEE: $ \rho: \mathbb R^n\times\mathbb R\to\mathbb R^n $ |
| @#55CCEE: context     | @#55CCEE: $ p \in C(\mathbb R^n\times\mathbb R,\mathbb R) $  |
| @#55CCEE: context     | @#55CCEE: $ \boldsymbol{\mathsf{T}} \in C(\mathbb R^n\times\mathbb R\times\mathbb R^n,\mathbb R^{n^2}) $  |
| @#55CCEE: context     | @#55CCEE: $ \mathbf{f} \in C(\mathbb R^n\times\mathbb R,\mathbb R^n) $  |
| @#DDDDDD: range       | @#DDDDDD: $ ::\rho(\mathbf{x},t)  $ |
| @#DDDDDD: range       | @#DDDDDD: $ ::p(\mathbf{x},t) $ |
| @#DDDDDD: range       | @#DDDDDD: $ ::\boldsymbol{\mathsf{T}}(\mathbf{x},t,\mathbf{v}) $ |
| @#DDDDDD: range       | @#DDDDDD: $ ::\mathbf{K}(\mathbf{x},t) $ |

| @#FFBB00: definiendum | @#FFBB00: $ \mathbf{v} \in \mathrm{it} $ |

| @#55EE55: postulate   | @#55EE55: $ \mathbf{v} \in C^2(\mathbb R^n\times\mathbb R,\mathbb R^n) $  |
| @#DDDDDD: range       | @#DDDDDD: $ ::\mathbf{v}(\mathbf{x},t) $ |

| @#55EE55: postulate   | @#55EE55: $ \rho\ \left(\frac{\partial}{\partial t} + \mathbf{v} \cdot \nabla  \right)\ \mathbf{v} = -\mathrm{grad}(p) + \nabla \cdot \boldsymbol{\mathsf{T}} + \mathbf{K} $ |

==== Discussion ====
==== Parents ====
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Navier_Stokes_Equations|Navier–Stokes equations]]
=== Subset of ===
[[PDE system]]
=== Related ===
[[Macroscopic observables from kinetic theory]]