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A Study of the Pressure Term in the ...

Payne, Michael R.

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A Study of the Pressure Term in the Navier-Stokes Equations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A Study of the Pressure Term in the Navier-Stokes Equations./
Author:	Payne, Michael R.
Description:	167 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
Contained By:	Dissertation Abstracts International75-02B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3601151
ISBN:	9781303517181

A Study of the Pressure Term in the Navier-Stokes Equations.
Payne, Michael R.

A Study of the Pressure Term in the Navier-Stokes Equations. - 167 p.

Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.

Thesis (Ph.D.)--The University of New Mexico, 2013.

In this paper we consider the Cauchy problem for the 3D NS equations for incompressible flows, and their solutions. We will discuss the results of a paper by Otto Kreiss and Jens Lorenz on the role of the pressure term in the NS equations, and its relationship to the fluid field u( x,t). The focus here is to concentrate on solutions to the equation where the fluid field u lies in the space C infinity( R3 ) ∩ Linfinity( R3 ), and not necessarily in L2( R3 ). If u(x,0) = f( x), where f ∈ Cinfinity ( R3 ) ∩ Linfinity( R3 ) we will consider the solutions for all t in time interval 0 ≤ t < T(f). In the original paper, estimates for the derivatives of the pressure were proved, but the definition of the pressure proved unsatisfactory due to the possibility of the divergence of the pressure term. The main object of this paper is to use the theory of singular integrals and the space of functions of BMO to properly address the pressure. In doing so, we will provide estimates on pressure term itself. This will allow us to strengthen the results of the original paper, and rigorously extend all results from the original paper to any function u ∈ Cinfinity( R3 ) ∩ Linfinity( R3 ).

ISBN: 9781303517181Subjects--Topical Terms:

515831
Mathematics.

A Study of the Pressure Term in the Navier-Stokes Equations.
LDR:02089nam a2200277 4500 001 1960800
005 20140624210011.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303517181
035 $a (MiAaPQ)AAI3601151
035 $a AAI3601151
040 $a MiAaPQ $c MiAaPQ
100 1 $a Payne, Michael R. $3 2096531
245 1 2 $a A Study of the Pressure Term in the Navier-Stokes Equations.
300 $a 167 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
500 $a Adviser: Jens Lorenz.
502 $a Thesis (Ph.D.)--The University of New Mexico, 2013.
520 $a In this paper we consider the Cauchy problem for the 3D NS equations for incompressible flows, and their solutions. We will discuss the results of a paper by Otto Kreiss and Jens Lorenz on the role of the pressure term in the NS equations, and its relationship to the fluid field u( x,t). The focus here is to concentrate on solutions to the equation where the fluid field u lies in the space C infinity( R3 ) ∩ Linfinity( R3 ), and not necessarily in L2( R3 ). If u(x,0) = f( x), where f ∈ Cinfinity ( R3 ) ∩ Linfinity( R3 ) we will consider the solutions for all t in time interval 0 ≤ t < T(f). In the original paper, estimates for the derivatives of the pressure were proved, but the definition of the pressure proved unsatisfactory due to the possibility of the divergence of the pressure term. The main object of this paper is to use the theory of singular integrals and the space of functions of BMO to properly address the pressure. In doing so, we will provide estimates on pressure term itself. This will allow us to strengthen the results of the original paper, and rigorously extend all results from the original paper to any function u ∈ Cinfinity( R3 ) ∩ Linfinity( R3 ).
590 $a School code: 0142.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a The University of New Mexico. $b Multicultural Teacher and Childhood Education. $3 2096532
773 0 $t Dissertation Abstracts International $g 75-02B(E).
790 $a 0142
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3601151