GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

doi:10.1007/s10473-021-0109-1

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 164-176.doi: 10.1007/s10473-021-0109-1

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

Muhammad Zainul ABIDIN, 陈杰诚

College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2019-09-16 修回日期:2020-05-30 出版日期:2021-02-25 发布日期:2021-04-06
通讯作者: Jiecheng CHEN E-mail:jcchen@zjnu.edu.cn
作者简介:Muhammad Zainul ABIDIN,E-mail:zainbs359@gmail.com
基金资助:
The research was supported by NSFC (11671363, 11701519).

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

Muhammad Zainul ABIDIN, Jiecheng CHEN

College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

Received:2019-09-16 Revised:2020-05-30 Online:2021-02-25 Published:2021-04-06
Contact: Jiecheng CHEN E-mail:jcchen@zjnu.edu.cn
About author:Muhammad Zainul ABIDIN,E-mail:zainbs359@gmail.com
Supported by:
The research was supported by NSFC (11671363, 11701519).

摘要/Abstract

摘要： In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{s(\cdot)}(\mathbb{R}^3)$ with $s(\cdot) = 4-2\alpha-\frac{3}{p(\cdot)} $. We prove global well-posedness result with small initial data belonging to $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{4-2\alpha-\frac{3}{p(\cdot)} }(\mathbb{R}^3)$. The result of this paper extends some recent work.

关键词: fractional Navier-Stokes equations, global well-posedness, Fourier-Besov-Morrey space

Abstract: In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{s(\cdot)}(\mathbb{R}^3)$ with $s(\cdot) = 4-2\alpha-\frac{3}{p(\cdot)} $. We prove global well-posedness result with small initial data belonging to $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{4-2\alpha-\frac{3}{p(\cdot)} }(\mathbb{R}^3)$. The result of this paper extends some recent work.

Key words: fractional Navier-Stokes equations, global well-posedness, Fourier-Besov-Morrey space

中图分类号:

35Q30

Muhammad Zainul ABIDIN, 陈杰诚. GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES[J]. 数学物理学报(英文版), 2021, 41(1): 164-176.

Muhammad Zainul ABIDIN, Jiecheng CHEN. GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES[J]. Acta mathematica scientia,Series B, 2021, 41(1): 164-176.

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GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

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