| Abstract: |
| For an arbitrary smooth initial datum, we construct multiple nonzero solutions to the 2D Navier-Stokes equations, with their gradients in the Hardy space $\mathcal{H}^p$ with any $p\in (0,1)$. Thus, in terms of the path space $C(\mathcal{H}^p)$ for vorticity, $p=1$ is the threshold value distinguishing between non-uniqueness and uniqueness regimes. In order to obtain our result, we develop the needed theory of Hardy spaces on periodic domains. |
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