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Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions

Im, Jeong Sook
http://rave.ohiolink.edu/etdc/view?acc_num=osu1281472399

Abstract Details

2010, Doctor of Philosophy, Ohio State University, Mathematics.
The standard mathematical model for the motion of surface waves in shallow water is the Euler equations for inviscid, incompressible flow, supplemented by free surface conditions. Without known explicit solutions in a simple form, simplifying assumptions are invoked to derive weakly nonlinear models and other variants that describe wave propagation. These models have provided good results in various applications, but their region of validity is not known precisely. The goal in this thesis is to assess the asymptotic errors in the KdV model by computing solutions to Euler’s equations numerically and comparing them with the predictions from the KdV equation directly.
Gregory Baker, PhD (Advisor)
Saleh Tanveer, PhD (Committee Member)
Ching-Shan Chou, PhD (Committee Member)
129 p.
Mathematics
Shallow water waves; KdV equation; Euler equations; Approximation; Singularities

Recommended Citations

Citations

  • Im, J. S. (2010). Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281472399

    APA Style (7th edition)

  • Im, Jeong Sook. Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions. 2010. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1281472399.

    MLA Style (8th edition)

  • Im, Jeong Sook. "Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281472399

    Chicago Manual of Style (17th edition)

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