Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842766 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 20 Pages |
Abstract
In this paper, we analyze a tamed 3D Navier–Stokes equation in uniform C2C2-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation. In particular, if there exists a bounded solution to the classical 3D Navier–Stokes equation, then this solution satisfies our tamed equation. Moreover, the existence of a global attractor for the tamed equation in bounded domains is also proved. As a simple application, we obtain that the set of all initial values for which the classical Navier–Stokes equation admits a bounded strong solution is open in H2.
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Authors
Xicheng Zhang,