The second iterate for the Navier-Stokes equation

Pierre Germain

doi:10.1016/j.jfa.2008.07.014

The second iterate for the Navier-Stokes equation

Pierre Germain

Mathematics

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

Abstract

We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak-strong uniqueness for Koch-Tataru solutions; and finally an instability result in over(B, ̇)_{∞, q}^-1, for q > 2.

Original language	English (US)
Pages (from-to)	2248-2264
Number of pages	17
Journal	Journal of Functional Analysis
Volume	255
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2008.07.014
State	Published - Nov 1 2008

Keywords

Bilinear operators
Navier-Stokes
Weak-strong uniqueness
Well-posedness

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2008.07.014

Cite this

@article{5a32ad55e6b5488aa09a7f281e5ddfc8,

title = "The second iterate for the Navier-Stokes equation",

abstract = "We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak-strong uniqueness for Koch-Tataru solutions; and finally an instability result in over(B,{\. })∞, q-1, for q > 2.",

keywords = "Bilinear operators, Navier-Stokes, Weak-strong uniqueness, Well-posedness",

author = "Pierre Germain",

year = "2008",

month = nov,

day = "1",

doi = "10.1016/j.jfa.2008.07.014",

language = "English (US)",

volume = "255",

pages = "2248--2264",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "9",

}

TY - JOUR

T1 - The second iterate for the Navier-Stokes equation

AU - Germain, Pierre

PY - 2008/11/1

Y1 - 2008/11/1

N2 - We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak-strong uniqueness for Koch-Tataru solutions; and finally an instability result in over(B, ̇)∞, q-1, for q > 2.

AB - We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak-strong uniqueness for Koch-Tataru solutions; and finally an instability result in over(B, ̇)∞, q-1, for q > 2.

KW - Bilinear operators

KW - Navier-Stokes

KW - Weak-strong uniqueness

KW - Well-posedness

UR - http://www.scopus.com/inward/record.url?scp=58049164748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049164748&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2008.07.014

DO - 10.1016/j.jfa.2008.07.014

M3 - Article

AN - SCOPUS:58049164748

SN - 0022-1236

VL - 255

SP - 2248

EP - 2264

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

The second iterate for the Navier-Stokes equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this