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navier-stokes_equations [2013/11/10 19:57]
nikolaj
navier-stokes_equations [2014/03/21 11:11] (current)
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 ===== Navier–Stokes equations ===== ===== Navier–Stokes equations =====
-==== Definition ​====+==== Set ====
  
-| @#88DDEE: $ n\in\mathbb N $ | +| @#55CCEE: context ​    | @#55CCEE: $ n\in\mathbb N $ | 
-| @#88DDEE: $ \rho: \mathbb R^n\times\mathbb R\to\mathbb R^n $ | +| @#55CCEE: context ​    | @#55CCEE: $ \rho: \mathbb R^n\times\mathbb R\to\mathbb R^n $ | 
-| @#88DDEE: $ p \in C(\mathbb R^n\times\mathbb R,\mathbb R) $  | +| @#55CCEE: context ​    | @#55CCEE: $ 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}) $  | +| @#55CCEE: context ​    | @#55CCEE: $ \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) $  | +| @#55CCEE: context ​    | @#55CCEE: $ \mathbf{f} \in C(\mathbb R^n\times\mathbb R,\mathbb R^n) $  | 
-| @#DDDDDD: $ ::​\rho(\mathbf{x},​t) ​ $ | +| @#DDDDDD: range       | @#DDDDDD: $ ::​\rho(\mathbf{x},​t) ​ $ | 
-| @#DDDDDD: $ ::​p(\mathbf{x},​t) $ | +| @#DDDDDD: range       | @#DDDDDD: $ ::​p(\mathbf{x},​t) $ | 
-| @#DDDDDD: $ ::​\boldsymbol{\mathsf{T}}(\mathbf{x},​t,​\mathbf{v}) $ | +| @#DDDDDD: range       | @#DDDDDD: $ ::​\boldsymbol{\mathsf{T}}(\mathbf{x},​t,​\mathbf{v}) $ | 
-| @#DDDDDD: $ ::​\mathbf{K}(\mathbf{x},​t) $ |+| @#DDDDDD: range       | @#DDDDDD: $ ::​\mathbf{K}(\mathbf{x},​t) $ |
  
-| @#FFBB00: $ \mathbf{v} \in \mathrm{it} $ |+| @#FFBB00: definiendum ​| @#FFBB00: $ \mathbf{v} \in \mathrm{it} $ |
  
-| @#55EE55: $ \mathbf{v} \in C^2(\mathbb R^n\times\mathbb R,\mathbb R^n) $  | +| @#55EE55: postulate ​  | @#55EE55: $ \mathbf{v} \in C^2(\mathbb R^n\times\mathbb R,\mathbb R^n) $  | 
-| @#DDDDDD: $ ::​\mathbf{v}(\mathbf{x},​t) $ |+| @#DDDDDD: range       | @#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} $ |+| @#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 ==== ==== Discussion ====
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 === Subset of === === Subset of ===
 [[PDE system]] [[PDE system]]
-=== Context ​===+=== Related ​===
 [[Macroscopic observables from kinetic theory]] [[Macroscopic observables from kinetic theory]]
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