Mixed variational problems associated with stationary viscous incompressible free boundary flows

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dc.contributor.advisorReddy, B Dayaen_ZA
dc.contributor.authorLe Roux, Christiaanen_ZA
dc.date.accessioned2015-12-28T06:03:37Z
dc.date.available2015-12-28T06:03:37Z
dc.date.issued1991en_ZA
dc.descriptionBibliography: pages 93-97.en_ZA
dc.description.abstractA strategy that is often used in the study of capillary free boundary (FB) problems for viscous incompressible flows is the following: (1) Ignore one of the boundary conditions at the FB and prove that for every chosen position of the FB the resultant problem, here called the auxiliary problem (AP), is well posed. (2) Establish regularity results for the solution of the AP. (3) Using (2) and the remaining boundary condition, determine the position of the FB. We study the existence and uniqueness of the weak solution(s) to the AP, i.e., step (1), under minimal regularity constraints on the data and domain. The analysis is carried out for stationary two-dimensional flows, governed by either the Stokes or Navier-Stokes equations, in the context of four standard examples. A Green's formula is derived which allows the AP to be formulated as a mixed variational problem in which the pressure and normal stress appear as Lagrange multipliers. Existence and uniqueness results are obtained by using the Ladyzhenskaya-Babuska-Brezzi theory for mixed problems. By analogy with step (3), the dependence of the normal stress on the position of the FB is investigated.en_ZA
dc.identifier.apacitationLe Roux, C. (1991). <i>Mixed variational problems associated with stationary viscous incompressible free boundary flows</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/15965en_ZA
dc.identifier.chicagocitationLe Roux, Christiaan. <i>"Mixed variational problems associated with stationary viscous incompressible free boundary flows."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1991. http://hdl.handle.net/11427/15965en_ZA
dc.identifier.citationLe Roux, C. 1991. Mixed variational problems associated with stationary viscous incompressible free boundary flows. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Le Roux, Christiaan AB - A strategy that is often used in the study of capillary free boundary (FB) problems for viscous incompressible flows is the following: (1) Ignore one of the boundary conditions at the FB and prove that for every chosen position of the FB the resultant problem, here called the auxiliary problem (AP), is well posed. (2) Establish regularity results for the solution of the AP. (3) Using (2) and the remaining boundary condition, determine the position of the FB. We study the existence and uniqueness of the weak solution(s) to the AP, i.e., step (1), under minimal regularity constraints on the data and domain. The analysis is carried out for stationary two-dimensional flows, governed by either the Stokes or Navier-Stokes equations, in the context of four standard examples. A Green's formula is derived which allows the AP to be formulated as a mixed variational problem in which the pressure and normal stress appear as Lagrange multipliers. Existence and uniqueness results are obtained by using the Ladyzhenskaya-Babuska-Brezzi theory for mixed problems. By analogy with step (3), the dependence of the normal stress on the position of the FB is investigated. DA - 1991 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1991 T1 - Mixed variational problems associated with stationary viscous incompressible free boundary flows TI - Mixed variational problems associated with stationary viscous incompressible free boundary flows UR - http://hdl.handle.net/11427/15965 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/15965
dc.identifier.vancouvercitationLe Roux C. Mixed variational problems associated with stationary viscous incompressible free boundary flows. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1991 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15965en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleMixed variational problems associated with stationary viscous incompressible free boundary flowsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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