Energy methods for fractional Navier-Stokes equations

被引：16

作者：

Zhou, Yong ^{[1
,2
]}

Peng, Li ^{[1
]}

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; Energy methods; Approximate solutions; MILD SOLUTIONS; EVOLUTION INCLUSIONS; MORREY SPACES; EXISTENCE;

D O I：

10.1016/j.chaos.2017.03.053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we make use of energy methods to study the Navier-Stokes equations with time-fractional derivative. Such equations can be used to simulate anomalous diffusion in fractal media. In the first step, we construct a regularized equation by using a smoothing process to transform unbounded differential operators into bounded operators and then obtain the approximate solutions. The second part describes a procedure to take a limit in the approximation program to present a global solution to the objective equation. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：78 / 85

页数：8

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