Navier–Stokes equations
Set
| context | $ n\in\mathbb N $ |
| context | $ \rho: \mathbb R^n\times\mathbb R\to\mathbb R^n $ |
| context | $ p \in C(\mathbb R^n\times\mathbb R,\mathbb 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} $ |
Discussion
Parents
Reference
Subset of
