What does $\nabla\times u$ mean in distributions?

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What does $\nabla\times u$ mean in distributions?

Like obviously we associate $\nabla u\to\forall\varphi\in\mathcal{S}(\mathbb{R}):\langle -\nabla\varphi,u\rangle$ but what if $u(x,t)\in\mathbb{R}^3$ and we were looking at the curl instead$?$