Navier–Stokes equations
Set
| context | n∈N |
| context | ρ:Rn×R→Rn |
| context | p∈C(Rn×R,R) |
| context | \boldsymbol{\mathsf{T}} \in C(\mathbb R^n\times\mathbb R\times\mathbb R^n,\mathbb R^{n^2}) |
| context | \mathbf{f} \in C(\mathbb R^n\times\mathbb R,\mathbb R^n) |
| range | ::\rho(\mathbf{x},t) |
| range | ::p(\mathbf{x},t) |
| range | ::\boldsymbol{\mathsf{T}}(\mathbf{x},t,\mathbf{v}) |
| range | ::\mathbf{K}(\mathbf{x},t) |
| definiendum | \mathbf{v} \in \mathrm{it} |
| postulate | \mathbf{v} \in C^2(\mathbb R^n\times\mathbb R,\mathbb R^n) |
| range | ::\mathbf{v}(\mathbf{x},t) |
| postulate | \rho\ \left(\frac{\partial}{\partial t} + \mathbf{v} \cdot \nabla \right)\ \mathbf{v} = -\mathrm{grad}(p) + \nabla \cdot \boldsymbol{\mathsf{T}} + \mathbf{K} |
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