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Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems

Kim, Tae Eun
http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Mathematics.
In this thesis, we investigate a steady translating pair of two-dimensional finite-area uniform vortex cores with equal and opposite vorticities surrounded by a homogeneous inviscid irrotational incompressible fluid flow. The governing equations and constraints of this idealized physical phenomenon give rise to a mathematical structure that is nonlinear by nature, more precisely, a nonlinear integro-differential equation for a periodic function. Following the quasi-solution scheme, a numerically obtained approximate analytical solution is used to prove rigorously the existence and uniqueness of the system of a steady-state vortex pair.
Saleh Tanveer (Advisor)
Ovidu Costin (Committee Member)
Edward Overman (Committee Member)
108 p.
Fluid Dynamics; Mathematics

Recommended Citations

Citations

  • Kim, T. E. (2017). Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532

    APA Style (7th edition)

  • Kim, Tae Eun. Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532.

    MLA Style (8th edition)

  • Kim, Tae Eun. "Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532

    Chicago Manual of Style (17th edition)

osu1499793039477532
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This open access ETD is published by The Ohio State University and OhioLINK.