Abstract
In this paper we give optimal lower bounds for the blow-up rate of the \(\dot{H}^{s}\left( \mathbb {T}^3\right) \)-norm, \(\frac{1}{2}<s<\frac{5}{2}\), of a putative singular solution of the Navier–Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when \(s>\frac{5}{2}\).
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Communicated by D. Chae
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Cortissoz, J.C., Montero, J.A. Lower Bounds for Possible Singular Solutions for the Navier–Stokes and Euler Equations Revisited. J. Math. Fluid Mech. 20, 1–5 (2018). https://doi.org/10.1007/s00021-016-0308-z
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DOI: https://doi.org/10.1007/s00021-016-0308-z