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On the regularity of a model non-Newtonian fluid Maxwell, David Aquilla
Abstract
Existence and regularity of steady and unsteady solutions of a PDE describing the motion of a prototypical incompressible fluid with shear dependent viscosity are studied. The regularity theory is approached by studying the associated elliptic operator. A summary of the classical technique of difference quotients applied to non-linear elliptic systems is given by applying it to the elliptic system associated with a vector Burgers-like system. Interior regularity is proved for a general class of Stokes-like elliptic operators using a new solenoidal test function that permits the application difference quotient methods to systems with a divergence free constraint. Existence for steady solutions of the incompressible fluid PDE is proven; interior regularity follows immediately from regularity of the Stokes-like elliptic system. Existence and interior regularity for time dependent solutions are proven.
Item Metadata
Title |
On the regularity of a model non-Newtonian fluid
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1997
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Description |
Existence and regularity of steady and unsteady solutions of a PDE describing the motion
of a prototypical incompressible fluid with shear dependent viscosity are studied.
The regularity theory is approached by studying the associated elliptic operator. A
summary of the classical technique of difference quotients applied to non-linear elliptic
systems is given by applying it to the elliptic system associated with a vector
Burgers-like system. Interior regularity is proved for a general class of Stokes-like
elliptic operators using a new solenoidal test function that permits the application difference
quotient methods to systems with a divergence free constraint. Existence for
steady solutions of the incompressible fluid PDE is proven; interior regularity follows
immediately from regularity of the Stokes-like elliptic system. Existence and interior
regularity for time dependent solutions are proven.
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Extent |
3227947 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-03-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0079973
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1997-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.