Dr. Ryan Thompson

Associate Professor of Mathematics


Ryan Thompson

For over a decade, I have worked as a mathematician and have dedicated my academic life to the study of partial differential equations (PDEs). Through these particular mathematical lenses, I have analyzed the evolutionary processes of solutions that these equations yield. In particular, my research has been dedicated to shallow water wave theory, which is the analysis of water waves and how they evolve with time over a flat shallow bottom. Since at the heart of this field lies fluid mechanics and dynamics, I've not only studied these shallow water wave models, but also the models of hydrodynamics from which these equations originate such as the Euler and Navier-Stokes equations. My research in these areas have ultimately led to my fascination with the evolution of fluid motion, and I have continued to exercise great diligence in making contributions to PDEs.

I also really enjoy the teaching aspect of academia. From my early days as a tutor in the math lab at North Georgia College & State University to teaching at the University of Notre Dame, I have developed and honed a remarkable pedagogy in order to deliver my students a proper education. Through the strategies I employ, none of my students are left behind, and before leaving my classroom, they obtain a thorough and deeper understanding of mathematics.

On and off the blackboard, my diligence towards education has paid huge dividends. Not only do I promote a collaborative environment in the classroom, but also among my colleagues. With a firm belief in education as a team effort, I have always striven to mollify the bureacratic end so as not to interfere with the actual education of students. Constant communication is kept between my colleagues so as to deliver the proper mathematical materials in the classroom. The end result being that our students' mathematical capacity is amplified, and they evolve into the brightest of individuals.


  • Ph.D., Mathematics, University of Notre Dame, 2015
  • M.S., Mathematics, University of Notre Dame, 2012
  • B.S., Mathematics, North Georgia College and State University, 2009
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Research Interests

  • Partial Differential Equations
  • Fluid Dynamics
  • Linear and Nonlinear Dispersive PDEs
  • Linear and Nonlinear Evolution Equations

    • J. Holmes, R. C. Thompson, F. Tiǧlay, The Cauchy Problem for the Gurevich-Zybin System, Journal of Mathematical Physics, 63, No. 4 (2022).
    • J. Holmes, R. C. Thompson, F. Tiǧlay, Continuity of the Data-to-Solution Map for the FORQ Equation in Besov Spaces, Journal of Differential and Integral Equations, 34, No. 5-6 (2021), 295-314.
    • J. Holmes, R. C. Thompson, F. Tiǧlay, Nonuniform Dependence of the R-b-family system in Besov Spaces, Zeitschrift für Angewandte Mathematik und Mechanik (Journal of Applied Mathematics and Mechanics), https://doi.org/10.1002/zamm.202000329 (2021).
    • R.C. Thompson, The Cauchy Problem for the 1-D Gurevich-Zybin System, Journal of Mathematical Physics, 60, No. 5 (2019).
    • J. Holmes, R. C. Thompson, Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces, Journal of Differential Equations, 263 No. 7 (2017), 4355-4381.
    • R. C. Thompson, Decay Properties of Solutions to a 4-parameter Family of Wave Equations, Journal of Mathematical Analysis and Applications, 451 (2017), 393-404.
    • J. Holmes, R. C. Thompson, Classical Solutions to the Generalized Camassa-Holm Equation, Journal of Advances in Differential Equations, 22 No. 5-6, (2017), 339-362.
    • A. Himonas, R. C. Thompson, Persistence properties and unique continuation for a generalized Camassa-Holm equation, Journal of Mathematical Physics, 55 091503 (2014).
    • R. C. Thompson, The periodic Cauchy problem for the 2-component Camassa-Holm system, Differential and Integral Equations, 26 (2013), 155-182.


    Dr. Ryan Thompson CV


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Contact me at ryan.thompson@ung.edu.