### A Tamed 3D Navier-Stokes Equation in DomainsA Tamed 3D Navier-Stokes Equation in Domains

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 Author Zhang, Xicheng Source arXiv.org Content type Text File Format PDF Date of Submission 2008-06-10 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Analysis of PDEs ♦ Mathematics - Dynamical Systems ♦ math Abstract In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform $C^2$-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 simple applications, some well known results for the classical Navier-Stokes equations in unbounded domains are covered. Educational Use Research Learning Resource Type Article