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The solution satisfies the natural bounds $Q\\in L^\\infty_tH^1_x\\cap L^2_tH^2_x$ and $u\\in L^\\infty_tL^2_x\\cap L^2_tH^1_x$, the distributional form of the equations, and the expanded Leray--Hopf type energy inequality used in weak--strong uniqueness arguments. The proof does not pass directly to the limit in that expanded inequality, where the non-corotational terms contain products of the form $|Q^n|^4Q^n:\\nabla u^n$. 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