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Existence of locally momentum conser...

Youngs, Matthias.

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Existence of locally momentum conserving solutions to a model for heat conducting flow.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Existence of locally momentum conserving solutions to a model for heat conducting flow./
Author:	Youngs, Matthias.
Description:	93 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
Contained By:	Dissertation Abstracts International74-10B(E).
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3587514
ISBN:	9781303247903

Existence of locally momentum conserving solutions to a model for heat conducting flow.
Youngs, Matthias.

Existence of locally momentum conserving solutions to a model for heat conducting flow. - 93 p.

Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.

Thesis (Ph.D.)--Indiana University, 2013.

In this thesis, we consider a mathematical model to describe and analyze a compressible, heat conducting fluid flow. The fluid is described by the density, velocity, and temperature functions which will evolve on a changing density support of the fluid. The model is constructed for locally momentum conserving solutions. That is, if a fluid packet is isolated from spatial walls and other fluid packets on a time interval, then on that interval the momentum of the isolated packet is conserved. We appeal to the compressible Navier-Stokes equations for a heat conducting flow to describe the evolution of the density, velocity, and temperature of the fluid on the fluid region. However, the model must accommodate discontinuities that may arise. For example, we could have a fluid with infinitely many initial fluid packets that collide at infinitely many collision times that have a finite accumulation point. The model requires solutions with minimal regularity that still reflect the locally momentum conserving property discussed above.

ISBN: 9781303247903Subjects--Topical Terms:

1669109
Applied Mathematics.

Existence of locally momentum conserving solutions to a model for heat conducting flow.
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100 1 $a Youngs, Matthias. $3 2096792
245 1 0 $a Existence of locally momentum conserving solutions to a model for heat conducting flow.
300 $a 93 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
500 $a Adviser: David Hoff.
502 $a Thesis (Ph.D.)--Indiana University, 2013.
520 $a In this thesis, we consider a mathematical model to describe and analyze a compressible, heat conducting fluid flow. The fluid is described by the density, velocity, and temperature functions which will evolve on a changing density support of the fluid. The model is constructed for locally momentum conserving solutions. That is, if a fluid packet is isolated from spatial walls and other fluid packets on a time interval, then on that interval the momentum of the isolated packet is conserved. We appeal to the compressible Navier-Stokes equations for a heat conducting flow to describe the evolution of the density, velocity, and temperature of the fluid on the fluid region. However, the model must accommodate discontinuities that may arise. For example, we could have a fluid with infinitely many initial fluid packets that collide at infinitely many collision times that have a finite accumulation point. The model requires solutions with minimal regularity that still reflect the locally momentum conserving property discussed above.
520 $a The proof of existence of such weak solutions is outlined as follows. For the general case where the initial support of the fluid is a countable union of disjoint fluid packets, truncate the initial fluid support to be a finite union. We argue for the existence of an approximate solution. We then make classical and novel compactness arguments to show that as the number of fluid packets approaches infinity, we obtain a weak solution that is locally momentum conserving. Only the most basic of bounds are independent of the number of initial fluid packets. Therefore this compactness is very weak. The limit will have minimal regularity, but still reflect desired physical properties.
590 $a School code: 0093.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a Indiana University. $b Mathematics. $3 1036206
773 0 $t Dissertation Abstracts International $g 74-10B(E).
790 $a 0093
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3587514