Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592017 | Journal of Functional Analysis | 2008 | 15 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory