The Cauchy problem for fractional Navier-Stokes equations in Sobolev spaces

被引：9

作者：

Peng, Li ^{[1
]}

Zhou, Yong ^{[1
,2
]}

Ahmad, Bashir ^{[2
]}

Alsaedi, Ahmed ^{[2
]}

机构：

[1] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

来源：

CHAOS SOLITONS & FRACTALS | 2017年 / 102卷

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; Caputo fractional derivative; Cauchy problem; Sobolev space; Existence; MILD SOLUTIONS; TIME; CONTROLLABILITY; EXISTENCE;

D O I：

10.1016/j.chaos.2017.02.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we use the tools from harmonic analysis to study the Cauchy problem for Navier-Stokes equations with time-fractional derivative of order a. (0, 1), which can be used to simulate the anomalous diffusion in fractal media. Two main results concerning the local existence of solutions for the given problem in Sobolev space are addressed. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：218 / 228

页数：11

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