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• W2964200067 abstract "We prove that the Cauchy problem for the three-dimensional Navier–Stokes equations is ill-posed in B ˙ ∞ − 1 , ∞ in the sense that a “norm inflation” happens in finite time. More precisely, we show that initial data in the Schwartz class S that are arbitrarily small in B ˙ ∞ − 1 , ∞ can produce solutions arbitrarily large in B ˙ ∞ − 1 , ∞ after an arbitrarily short time. Such a result implies that the solution map itself is discontinuous in B ˙ ∞ − 1 , ∞ at the origin." @default.
• W2964200067 created "2019-07-30" @default.
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• W2964200067 date "2008-11-01" @default.
• W2964200067 modified "2023-10-06" @default.
• W2964200067 title "Ill-posedness of the Navier–Stokes equations in a critical space in 3D" @default.
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• W2964200067 doi "https://doi.org/10.1016/j.jfa.2008.07.008" @default.
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