  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 $\displaystyle \nabla p = \nabla \left(\sum_{i,j=1}^d
\mathcal{R}_i \mathcal{R}_j (u_i u_j - F_{i,j}) \right)$, 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.
