Ill-posedness of the Navier–Stokes equations in a critical space in 3D
نویسندگان
چکیده
We prove that the Cauchy problem for the three-dimensional Navier–Stokes equations is ill-posed in Ḃ −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 Ḃ−1,∞ ∞ can produce solutions arbitrarily large in Ḃ−1,∞ ∞ after an arbitrarily short time. Such a result implies that the solution map itself is discontinuous in Ḃ−1,∞ ∞ at the origin. © 2008 Elsevier Inc. All rights reserved.
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