Ill-posedness of the Navier-Stokes equations in a critical space in 3D |
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| Authors: | Jean Bourgain Nataša Pavlovi? |
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| Institution: | a School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA
b Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712, USA |
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| Abstract: | We prove that the Cauchy problem for the three-dimensional Navier-Stokes equations is ill-posed in  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  can produce solutions arbitrarily large in  after an arbitrarily short time. Such a result implies that the solution map itself is discontinuous in  at the origin. |
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| Keywords: | Navier-Stokes equations Ill-posedness |
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