On the local solvability of the initial-boundary value problem of fiber spinning of the upper convected Maxwell fluid

Identifier

75

Author

Dias Kurmashev

Date

2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematical Sciences

Concentration

Mathematics

Committee Chair

Thomas Hagen

Committee Member

Anna H Kaminska

Committee Member

James E Jamison

Committee Member

Alistair Windsor

Abstract

The fiber spinning process of a viscoelastic liquid modeled by the constitutive theory of the Maxwell fluid is analyzed.The governing equations are given by one- dimensional mass, momentum, and constitutive equations which arise in the slender bodyapproximation by cross-sectional averaging of the two-dimensional axisymmetric Stokes equationswith free boundary. Existence, uniqueness, andregularity results are proved by means of fixed point arguments, energy estimates, and weak/weak* convergence methods.The complexity in this problem lies with the constitutive model of the Maxwell fluid: when both the outflow velocity at the spinneret andthe pulling velocity at take-upare prescribed, a boundary condition can be imposed for only one of the two elastic stress components at the inlet. The absence ofthe second stress boundary condition makes the mathematical analysis of the problem difficult.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

Recommended Citation

Kurmashev, Dias, "On the local solvability of the initial-boundary value problem of fiber spinning of the upper convected Maxwell fluid" (2010). Electronic Theses and Dissertations. 49.
https://digitalcommons.memphis.edu/etd/49