Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk

S. Rahman; T. Hayat; B. Ahmad

doi:10.1007/s13324-016-0132-x

Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk

S. Rahman
, T. Hayat
, B. Ahmad

COMSATS University Islamabad
Northwestern Polytechnical University Xian
Quaid-I-Azam University
Faculty of Sciences, King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when ∥F&∥²BMO, ∥g∥²BMO, ∥∂g∂y∥²_BMO and ∥∂2g∂y²∥²BMO are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and g=∇×F=∂F∂z is the vorticity of the rotating fluid.

Original language	English
Pages (from-to)	93-105
Number of pages	13
Journal	Analysis and Mathematical Physics
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/s13324-016-0132-x
State	Published - 1 Mar 2017
Externally published	Yes

Keywords

MHD equations
Regularity criteria
Rotating frame
Third grade fluid

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title = "Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk",

abstract = "The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when ∥F\&∥2BMO, ∥g∥2BMO, ∥∂g∂y∥2BMO and ∥∂2g∂y2∥2BMO are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and g=∇×F=∂F∂z is the vorticity of the rotating fluid.",

keywords = "MHD equations, Regularity criteria, Rotating frame, Third grade fluid",

author = "S. Rahman and T. Hayat and B. Ahmad",

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doi = "10.1007/s13324-016-0132-x",

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T1 - Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk

AU - Rahman, S.

AU - Hayat, T.

AU - Ahmad, B.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when ∥F&∥2BMO, ∥g∥2BMO, ∥∂g∂y∥2BMO and ∥∂2g∂y2∥2BMO are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and g=∇×F=∂F∂z is the vorticity of the rotating fluid.

AB - The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when ∥F&∥2BMO, ∥g∥2BMO, ∥∂g∂y∥2BMO and ∥∂2g∂y2∥2BMO are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and g=∇×F=∂F∂z is the vorticity of the rotating fluid.

KW - MHD equations

KW - Regularity criteria

KW - Rotating frame

KW - Third grade fluid

UR - https://www.scopus.com/pages/publications/85011990083

U2 - 10.1007/s13324-016-0132-x

DO - 10.1007/s13324-016-0132-x

M3 - Article

AN - SCOPUS:85011990083

SN - 1664-2368

VL - 7

SP - 93

EP - 105

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 1

ER -

Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk

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