منابع مشابه
Rooted Trees for 3d Navier-stokes Equation
We establish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of this series recovering in a simplified manner some results obtained recently by Sinai and other known results. The series representation make sense also in the critical case where there exists global solutions for small initial data.
متن کاملTrees for Navier-stokes
We estabilish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of the series so obtained recovering in a simplified manner some results obtained recently by Sinai and other known results. In particular we extend the series representation of Sinai to the critical case where there exists global so...
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In this article, a non linear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier-Stokes equation) to a critical space (invariant through the canonical scaling of the Navier-Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier-Stokes equations. Tho...
متن کاملA Tamed 3d Navier-stokes Equation in Domains
In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform C-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 exi...
متن کاملTamed 3d Navier-stokes Equation: Existence, Uniqueness and Regularity
In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, using this renomalized equation we can give a new construction for a suitable weak solution of the classic...
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ژورنال
عنوان ژورنال: Dynamics of Partial Differential Equations
سال: 2006
ISSN: 1548-159X,2163-7873
DOI: 10.4310/dpde.2006.v3.n2.a3