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arXiv · 0806.1600

A Tamed 3D Navier-Stokes Equation in Domains

Xicheng Zhang
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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.

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Xicheng Zhang. 2008-06-10. A Tamed 3D Navier-Stokes Equation in Domains. https://arxiv.org/abs/0806.1600

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