Between homogeneous and inhomogeneous Navier–Stokes systems: The issue of stability

Piotr B. Mucha; Liutang Xue; Xiaoxin Zheng

doi:10.1016/j.jde.2019.01.012

Between homogeneous and inhomogeneous Navier–Stokes systems: The issue of stability

Piotr B. Mucha
, Liutang Xue^*
, Xiaoxin Zheng

^*Corresponding author for this work

School of Mathematical Sciences

University of Warsaw
Beijing Normal University

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

4 Scopus citations

Abstract

We construct large velocity vector solutions to the three dimensional inhomogeneous Navier–Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole R ³ .

Original language	English
Pages (from-to)	307-363
Number of pages	57
Journal	Journal of Differential Equations
Volume	267
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2019.01.012
State	Published - 15 Jun 2019

Keywords

2D homogeneous Navier–Stokes system
3D Inhomogeneous Navier–Stokes system
Lagrangian coordinates
Stability

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10.1016/j.jde.2019.01.012

Cite this

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title = "Between homogeneous and inhomogeneous Navier{\textendash}Stokes systems: The issue of stability",

abstract = " We construct large velocity vector solutions to the three dimensional inhomogeneous Navier{\textendash}Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole R 3 .",

keywords = "2D homogeneous Navier{\textendash}Stokes system, 3D Inhomogeneous Navier{\textendash}Stokes system, Lagrangian coordinates, Stability",

author = "Mucha, \{Piotr B.\} and Liutang Xue and Xiaoxin Zheng",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.jde.2019.01.012",

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T1 - Between homogeneous and inhomogeneous Navier–Stokes systems

T2 - The issue of stability

AU - Mucha, Piotr B.

AU - Xue, Liutang

AU - Zheng, Xiaoxin

PY - 2019/6/15

Y1 - 2019/6/15

N2 - We construct large velocity vector solutions to the three dimensional inhomogeneous Navier–Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole R 3 .

AB - We construct large velocity vector solutions to the three dimensional inhomogeneous Navier–Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole R 3 .

KW - 2D homogeneous Navier–Stokes system

KW - 3D Inhomogeneous Navier–Stokes system

KW - Lagrangian coordinates

KW - Stability

UR - https://www.scopus.com/pages/publications/85060181200

U2 - 10.1016/j.jde.2019.01.012

DO - 10.1016/j.jde.2019.01.012

M3 - 文章

AN - SCOPUS:85060181200

SN - 0022-0396

VL - 267

SP - 307

EP - 363

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Between homogeneous and inhomogeneous Navier–Stokes systems: The issue of stability

Abstract

Keywords

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