We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire d\documentclass[12pt]{minimal}
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\begin{document}$d$\end{document}-dimensional Euclidean space is determined by the formula ∇p=∇(∑i,j=1dRiRj(uiuj−Fi,j))\documentclass[12pt]{minimal}
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\begin{document}$\nabla p = \nabla \left (\sum _{i,j=1}^{d} \mathcal{R}_{i} \mathcal{R}_{j} (u_{i} u_{j} - F_{i,j}) \right )$\end{document}, where d∈{2,3}\documentclass[12pt]{minimal}
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\begin{document}$d \in \{2, 3\}$\end{document}, u:=(u1,…,ud)\documentclass[12pt]{minimal}
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\begin{document}${\textbf{u}} := (u_{1}, \ldots ,u_{d})$\end{document} is the fluid velocity, F:=(Fi,j)1≤i,j≤d\documentclass[12pt]{minimal}
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\begin{document}$\mathbb{F}:= (F_{i,j})_{1\le i,j\le d}$\end{document} is the forcing tensor, and for all k∈{1,…,d}\documentclass[12pt]{minimal}
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\begin{document}$k \in \{1, \ldots , d\}$\end{document}, Rk\documentclass[12pt]{minimal}
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\begin{document}$\mathcal{R}_{k}$\end{document} is the k\documentclass[12pt]{minimal}
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\begin{document}$k$\end{document}-th Riesz transform.
