On the time-fractional Navier-Stokes equations

被引：140

作者：

Zhou, Yong ^{[1
,2
]}

Peng, Li ^{[1
]}

机构：

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

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; Caputo fractional derivative; Mittag-Leffler functions; Mild solutions; Regularity; EXTERIOR DOMAINS; CAUCHY-PROBLEM; MILD SOLUTIONS; EXISTENCE; SPACES; LP;

D O I：

10.1016/j.camwa.2016.03.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the Navier-Stokes equations with time-fractional derivative of order alpha is an element of (0, 1). This type of equations can be used to simulate anomalous diffusion in fractal media. We establish the existence and uniqueness of local and global mild solutions in Jq. Meanwhile, we also give local mild solutions inh. Moreover, we prove the existence and regularity of classical solutions for such equations in J(q). (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：874 / 891

页数：18

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