The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity

Sagun Chanillo; Jean Van Schaftingen; Po Lam Yung

doi:10.1007/978-3-319-52742-0_2

The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity

Sagun Chanillo, Jean Van Schaftingen, Po Lam Yung^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Citation (Scopus)

Abstract

We study the incompressible two dimensional Navier–Stokes equation with initial vorticity in the homogeneous Sobolev space Ẇ^1,1(ℝ²). This complements our earlier work for the case when the initial vorticity is in the inhomogeneous Sobolev space W^1,1(ℝ²).

Original language	English
Title of host publication	Harmonic Analysis, Partial Differential Equations and Applications
Editors	Sagun Chanillo, Bruno Franchi, Guozhen Lu, Carlos Perez, Eric T. Sawyer
Place of Publication	Switzerland
Publisher	Birkhauser
Chapter	2
Pages	19-25
Number of pages	7
Edition	1
ISBN (Electronic)	978-3-319-52742-0
ISBN (Print)	978-3-319-52741-3, 978-3-319-84974-4
DOIs	https://doi.org/10.1007/978-3-319-52742-0_2
Publication status	Published - 2017
Externally published	Yes

Publication series

Name	Applied and Numerical Harmonic Analysis
Publisher	Springer
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

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10.1007/978-3-319-52742-0_2

Cite this

Chanillo, S., Van Schaftingen, J., & Yung, P. L. (2017). The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity. In S. Chanillo, B. Franchi, G. Lu, C. Perez, & E. T. Sawyer (Eds.), Harmonic Analysis, Partial Differential Equations and Applications (1 ed., pp. 19-25). (Applied and Numerical Harmonic Analysis). Birkhauser. https://doi.org/10.1007/978-3-319-52742-0_2

Chanillo, Sagun ; Van Schaftingen, Jean ; Yung, Po Lam. / The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity. Harmonic Analysis, Partial Differential Equations and Applications. editor / Sagun Chanillo ; Bruno Franchi ; Guozhen Lu ; Carlos Perez ; Eric T. Sawyer. 1. ed. Switzerland : Birkhauser, 2017. pp. 19-25 (Applied and Numerical Harmonic Analysis).

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title = "The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity",

abstract = "We study the incompressible two dimensional Navier–Stokes equation with initial vorticity in the homogeneous Sobolev space Ẇ1,1(ℝ2). This complements our earlier work for the case when the initial vorticity is in the inhomogeneous Sobolev space W1,1(ℝ2).",

keywords = "Incompressible flow, Sobolev space, Stoke flow, Stokes equation, Viscosity coefficient",

author = "Sagun Chanillo and {Van Schaftingen}, Jean and Yung, {Po Lam}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

doi = "10.1007/978-3-319-52742-0_2",

language = "English",

isbn = "978-3-319-52741-3",

series = "Applied and Numerical Harmonic Analysis",

publisher = "Birkhauser",

pages = "19--25",

editor = "Sagun Chanillo and Bruno Franchi and Guozhen Lu and Carlos Perez and Sawyer, {Eric T.}",

booktitle = "Harmonic Analysis, Partial Differential Equations and Applications",

address = "Switzerland",

edition = "1",

}

Chanillo, S, Van Schaftingen, J & Yung, PL 2017, The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity. in S Chanillo, B Franchi, G Lu, C Perez & ET Sawyer (eds), Harmonic Analysis, Partial Differential Equations and Applications. 1 edn, Applied and Numerical Harmonic Analysis, Birkhauser, Switzerland, pp. 19-25. https://doi.org/10.1007/978-3-319-52742-0_2

The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity. / Chanillo, Sagun; Van Schaftingen, Jean; Yung, Po Lam.
Harmonic Analysis, Partial Differential Equations and Applications. ed. / Sagun Chanillo; Bruno Franchi; Guozhen Lu; Carlos Perez; Eric T. Sawyer. 1. ed. Switzerland: Birkhauser, 2017. p. 19-25 (Applied and Numerical Harmonic Analysis).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity

AU - Chanillo, Sagun

AU - Van Schaftingen, Jean

AU - Yung, Po Lam

N1 - Publisher Copyright: © Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - We study the incompressible two dimensional Navier–Stokes equation with initial vorticity in the homogeneous Sobolev space Ẇ1,1(ℝ2). This complements our earlier work for the case when the initial vorticity is in the inhomogeneous Sobolev space W1,1(ℝ2).

AB - We study the incompressible two dimensional Navier–Stokes equation with initial vorticity in the homogeneous Sobolev space Ẇ1,1(ℝ2). This complements our earlier work for the case when the initial vorticity is in the inhomogeneous Sobolev space W1,1(ℝ2).

KW - Incompressible flow

KW - Sobolev space

KW - Stoke flow

KW - Stokes equation

KW - Viscosity coefficient

UR - http://www.scopus.com/inward/record.url?scp=85047298953&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-52742-0_2

DO - 10.1007/978-3-319-52742-0_2

M3 - Chapter

SN - 978-3-319-52741-3

SN - 978-3-319-84974-4

T3 - Applied and Numerical Harmonic Analysis

SP - 19

EP - 25

BT - Harmonic Analysis, Partial Differential Equations and Applications

A2 - Chanillo, Sagun

A2 - Franchi, Bruno

A2 - Lu, Guozhen

A2 - Perez, Carlos

A2 - Sawyer, Eric T.

PB - Birkhauser

CY - Switzerland

ER -

Chanillo S, Van Schaftingen J, Yung PL. The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity. In Chanillo S, Franchi B, Lu G, Perez C, Sawyer ET, editors, Harmonic Analysis, Partial Differential Equations and Applications. 1 ed. Switzerland: Birkhauser. 2017. p. 19-25. (Applied and Numerical Harmonic Analysis). Epub 2017 Feb 22. doi: 10.1007/978-3-319-52742-0_2

The Incompressible Navier Stokes Flow in Two Dimensions with Prescribed Vorticity

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