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
收藏
页码：78 / 85
页数：8
相关论文
共 50 条
  • [21] DIFFERENCE METHODS OF SOLVING NAVIER-STOKES EQUATIONS
    BRAILOVS.IY
    KUSKAVA, TV
    CHUDOV, LA
    INTERNATIONAL CHEMICAL ENGINEERING, 1970, 10 (02): : 228 - &
  • [22] Projection methods for the incompressible Navier-Stokes equations
    Zhang Qing-Hai
    Li Yang
    ACTA PHYSICA SINICA, 2021, 70 (13)
  • [23] CONVERGENCE OF LEGENDRE METHODS FOR NAVIER-STOKES EQUATIONS
    CHEN, ZT
    E, WN
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 1994, 12 (04) : 298 - 311
  • [24] Global attractor for the Navier-Stokes equations with fractional deconvolution
    Catania, Davide
    Morando, Alessandro
    Trebeschi, Paola
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04): : 811 - 848
  • [25] The Lp energy methods and decay for the compressible Navier-Stokes equations with capillarity
    Kawashima, Shuichi
    Shibata, Yoshihiro
    Xu, Jiang
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2021, 154 : 146 - 184
  • [26] CONVERGENCE OF LEGENDRE METHODS FOR NAVIER-STOKES EQUATIONS
    Chen Zheng-ting(Luoyang Educational Institute
    JournalofComputationalMathematics, 1994, (04) : 298 - 311
  • [27] On multigrid methods for the compressible Navier-Stokes equations
    Drikakis, D
    Iliev, O
    Vassileva, D
    LARGE-SCALE SCIENTIFIC COMPUTING, 2001, 2179 : 344 - 352
  • [28] Entropy Consistent Methods for the Navier-Stokes Equations
    Mohammed, Akmal Nizam
    Ismail, Farzad
    JOURNAL OF SCIENTIFIC COMPUTING, 2015, 63 (02) : 612 - 631
  • [29] Uniform analytic solutions for fractional Navier-Stokes equations
    Lou, Zhenzhen
    Yang, Qixiang
    He, Jianxun
    He, Kaili
    APPLIED MATHEMATICS LETTERS, 2021, 112
  • [30] Uniqueness of weak solutions for fractional Navier-Stokes equations
    Yong Ding
    Xiaochun Sun
    Frontiers of Mathematics in China, 2015, 10 : 33 - 51
12345