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| - | ===== Navier–Stokes equations ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $ n\in\mathbb N $ | | ||
| - | | @#88DDEE: $ \rho: \mathbb R^n\times\mathbb R\to\mathbb R^n $ | | ||
| - | | @#88DDEE: $ p \in C(\mathbb R^n\times\mathbb R,\mathbb R) $ | | ||
| - | | @#88DDEE: $ \boldsymbol{\mathsf{T}} \in C(\mathbb R^n\times\mathbb R\times\mathbb R^n,\mathbb R^{n^2}) $ | | ||
| - | | @#88DDEE: $ \mathbf{f} \in C(\mathbb R^n\times\mathbb R,\mathbb R^n) $ | | ||
| - | | @#DDDDDD: $ ::\rho(\mathbf{x},t) $ | | ||
| - | | @#DDDDDD: $ ::p(\mathbf{x},t) $ | | ||
| - | | @#DDDDDD: $ ::\boldsymbol{\mathsf{T}}(\mathbf{x},t,\mathbf{v}) $ | | ||
| - | | @#DDDDDD: $ ::\mathbf{K}(\mathbf{x},t) $ | | ||
| - | |||
| - | | @#FFBB00: $ \mathbf{v} \in \mathrm{it} $ | | ||
| - | |||
| - | | @#55EE55: $ \mathbf{v} \in C^2(\mathbb R^n\times\mathbb R,\mathbb R^n) $ | | ||
| - | | @#DDDDDD: $ ::\mathbf{v}(\mathbf{x},t) $ | | ||
| - | |||
| - | | @#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]] | ||
| - | === Context === | ||
| - | [[Macroscopic observables from kinetic theory]] | ||
