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.
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页码：78 / 85
页数：8
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