On the incompressible limit of the compressible Navier-Stokes equations.

Persistent Link:
http://hdl.handle.net/10150/185888
Title:
On the incompressible limit of the compressible Navier-Stokes equations.
Author:
Lin, Chi-Kun.
Issue Date:
1992
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Many interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Navier-Stokes equations.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Levermore, C.D.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleOn the incompressible limit of the compressible Navier-Stokes equations.en_US
dc.creatorLin, Chi-Kun.en_US
dc.contributor.authorLin, Chi-Kun.en_US
dc.date.issued1992en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractMany interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectNavier-Stokes equations.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLevermore, C.D.en_US
dc.contributor.committeememberGreenlee, W.M.en_US
dc.contributor.committeememberBayly, Bruce J.en_US
dc.contributor.committeememberMatthias, Allan D.en_US
dc.identifier.proquest9234885en_US
dc.identifier.oclc712789870en_US
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