Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space

Zhijie Nan; Xiaoxin Zheng

doi:10.1016/j.jde.2016.05.035

Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space

Zhijie Nan
, Xiaoxin Zheng^*

^*Corresponding author for this work

School of Mathematical Sciences

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

11 Scopus citations

Abstract

We study Cauchy problem of the 3D Navier–Stokes equations with hyper-dissipation. By using the Fourier localization technique, we prove that the system has a unique global solution for large initial data in a critical Fourier–Herz space. More importantly, the energy of this solution is infinite.

Original language	English
Pages (from-to)	3670-3703
Number of pages	34
Journal	Journal of Differential Equations
Volume	261
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2016.05.035
State	Published - 15 Sep 2016

Keywords

Fourier–Herz space
Global well-posedness
Infinite energy solution
Kato's algorithm
Navier–Stokes equations

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10.1016/j.jde.2016.05.035

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title = "Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space",

abstract = "We study Cauchy problem of the 3D Navier–Stokes equations with hyper-dissipation. By using the Fourier localization technique, we prove that the system has a unique global solution for large initial data in a critical Fourier–Herz space. More importantly, the energy of this solution is infinite.",

keywords = "Fourier–Herz space, Global well-posedness, Infinite energy solution, Kato's algorithm, Navier–Stokes equations",

author = "Zhijie Nan and Xiaoxin Zheng",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = sep,

day = "15",

doi = "10.1016/j.jde.2016.05.035",

language = "英语",

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journal = "Journal of Differential Equations",

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T1 - Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space

AU - Nan, Zhijie

AU - Zheng, Xiaoxin

PY - 2016/9/15

Y1 - 2016/9/15

N2 - We study Cauchy problem of the 3D Navier–Stokes equations with hyper-dissipation. By using the Fourier localization technique, we prove that the system has a unique global solution for large initial data in a critical Fourier–Herz space. More importantly, the energy of this solution is infinite.

AB - We study Cauchy problem of the 3D Navier–Stokes equations with hyper-dissipation. By using the Fourier localization technique, we prove that the system has a unique global solution for large initial data in a critical Fourier–Herz space. More importantly, the energy of this solution is infinite.

KW - Fourier–Herz space

KW - Global well-posedness

KW - Infinite energy solution

KW - Kato's algorithm

KW - Navier–Stokes equations

UR - https://www.scopus.com/pages/publications/84979681458

U2 - 10.1016/j.jde.2016.05.035

DO - 10.1016/j.jde.2016.05.035

M3 - 文章

AN - SCOPUS:84979681458

SN - 0022-0396

VL - 261

SP - 3670

EP - 3703

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space

Abstract

Keywords

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