Tamed 3D navierstokes equation: Existence, uniqueness and regularity

Michael Röckner; Xicheng Zhang

doi:10.1142/S0219025709003859

Tamed 3D navierstokes equation: Existence, uniqueness and regularity

Michael Röckner^*
, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

Abstract

In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D NavierStokes 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 tamed equation we can give a new construction for a suitable weak solution of the classical 3D NavierStokes equation introduced in Refs. 16 and 2.

Original language	English
Pages (from-to)	525-549
Number of pages	25
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	12
Issue number	4
DOIs	https://doi.org/10.1142/S0219025709003859
Publication status	Published - Dec 2009
Externally published	Yes

Keywords

Classical solution
Navier-Stokes equation
Suitable weak solution

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10.1142/S0219025709003859

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abstract = "In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D NavierStokes 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 tamed equation we can give a new construction for a suitable weak solution of the classical 3D NavierStokes equation introduced in Refs. 16 and 2.",

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N2 - In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D NavierStokes 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 tamed equation we can give a new construction for a suitable weak solution of the classical 3D NavierStokes equation introduced in Refs. 16 and 2.

AB - In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D NavierStokes 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 tamed equation we can give a new construction for a suitable weak solution of the classical 3D NavierStokes equation introduced in Refs. 16 and 2.

KW - Classical solution

KW - Navier-Stokes equation

KW - Suitable weak solution

UR - https://www.scopus.com/pages/publications/75649144982

U2 - 10.1142/S0219025709003859

DO - 10.1142/S0219025709003859

M3 - Article

AN - SCOPUS:75649144982

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JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 4

ER -

Tamed 3D navierstokes equation: Existence, uniqueness and regularity

Abstract

Keywords

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