On the Use of the Riesz Transforms to Determine the Pressure Term in the Incompressible Navier-Stokes Equations on the Whole Space
2021
We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire $d$
-dimensional Euclidean space is determined by the formula $\nabla p = \nabla \left (\sum _{i,j=1}^{d} \mathcal{R}_{i} \mathcal{R}_{j} (u_{i} u_{j} - F_{i,j}) \right )$
, where $d \in \{2, 3\}$
, ${\textbf{u}} := (u_{1}, \ldots ,u_{d})$
is the fluid velocity, $\mathbb{F}:= (F_{i,j})_{1\le i,j\le d}$
is the forcing tensor, and for all $k \in \{1, \ldots , d\}$
, $\mathcal{R}_{k}$
is the $k$
-th Riesz transform.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
11
References
0
Citations
NaN
KQI