Minimal initial data for potential Navier-Stokes singularities

W. Rusin; Vladimir Sverak

doi:10.1016/j.jfa.2010.09.009

Minimal initial data for potential Navier-Stokes singularities

W. Rusin, Vladimir Sverak

Mathematics

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

37 Scopus citations

Abstract

Assuming some initial data u₀∈Ḣ^1/2(R³) lead to a singularity for the 3d Navier-Stokes equations, we show that there are also initial data with the minimal Ḣ^1/2-norm which will produce a singularity.

Original language	English (US)
Pages (from-to)	879-891
Number of pages	13
Journal	Journal of Functional Analysis
Volume	260
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2010.09.009
State	Published - Feb 15 2011

Bibliographical note

Funding Information:
* Corresponding author. E-mail address: sverak@math.umn.edu (V. Šverák). 1 Supported in part by the Graduate School Dissertation Fellowship. 2 Supported in part by NSF Grant DMS-0800908.

Keywords

Minimal data
Navier-Stokes
Singularities

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abstract = "Assuming some initial data u0∈Ḣ1/2(R3) lead to a singularity for the 3d Navier-Stokes equations, we show that there are also initial data with the minimal Ḣ1/2-norm which will produce a singularity.",

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author = "W. Rusin and Vladimir Sverak",

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AU - Sverak, Vladimir

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AB - Assuming some initial data u0∈Ḣ1/2(R3) lead to a singularity for the 3d Navier-Stokes equations, we show that there are also initial data with the minimal Ḣ1/2-norm which will produce a singularity.

KW - Minimal data

KW - Navier-Stokes

KW - Singularities

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Minimal initial data for potential Navier-Stokes singularities

Abstract

Bibliographical note

Keywords

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