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Contact

Email: stevenson "at" princeton.edu

Publications and Preprints

1. Traveling wave solutions to the free boundary incompressible Navier-Stokes equations in the limit of vanishing capillarity.

   • Joint with Ian Tice. In preparation.

2. Desingularization of Kirchhoff elliptical vortices and nondegenerate steady rotating vortex patch solutions to the planar Euler equations.

   • Joint with Răzvan-Octavian Radu. In preparation.

3. Large traveling gravity waves for free boundary Darcy flow.

   • Joint with Huy Q. Nguyen. In preparation.

4. Gravity driven traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations.

   • Joint with Ian Tice. 2025.
   • arXiv.

5. Stationary wave solutions to two dimensional viscous shallow water equations: theory of small and large solutions.

   • Joint with Ian Tice. 2025.
   • arXiv.

6. Periodic gravity-capillary roll wave solutions to the inclined viscous shallow water equations in two dimensions.

   • 2024.
   • SIAM J. Math. Anal.
   • arXiv.

7. The traveling wave problem for the shallow water equations: well-posedness and the limits of vanishing viscosity and surface tension.

   • Joint with Ian Tice. 2023.
   • Commun. Math. Phys.
   • arXiv.

8. Well-posedness of the stationary and slowly traveling wave problem for the free boundary incompressible Navier-Stokes equations.

   • Joint with Ian Tice. 2023.
   • J. Funct. Anal.
   • arXiv.

9. Well-posedness of the traveling wave problem for the free boundary compressible Navier-Stokes equations.

   • Joint with Ian Tice. 2023.
   • arXiv.

10. Traveling wave solutions to the multilayer free boundary incompressible Navier-Stokes equations.

    • Joint with Ian Tice. 2020.
    • SIAM J. Math. Anal.
    • arXiv.

11. A truncated real interpolation method and characterizations of screened Sobolev spaces.

    • Joint with Ian Tice. 2020.
    • Commun. Pure Appl. Anal.
    • arXiv.

12. Analysis of micropolar fluids: existence of potential microflow solutions, nearby global-well-posedness, stability and attractiveness.

    • Joint with Ian Tice. 2020.
    • Acta Appl. Math.
    • arXiv.

Education

Doctor of Philosophy in Mathematics Candidate - Princeton University (August 2021-Present)

• Advisor: Alexandru Ionescu

Master of Science in Mathematics - Carnegie Mellon University (Oct 2019-May 2021)

• Honors Degree Program: undergraduate and master degree programs completed simultaneously

• Advisor: Ian Tice

• Thesis: Miscellaneous Analysis of Micropolar Fluids, Screened Sobolev Spaces, and Multilayer Free Boundary Incompressible Navier-Stokes Equations

Bachelor of Science in Mathematics - Carnegie Mellon University (August 2017 - May 2021)

• GPA: 4.00/4.00

• Mathematical Studies Program: honors undergraduate course sequence in analysis and algebra

• Minor in Physics

Awards, Grants, & Scholarships

• Princeton University Department of Mathematics Merit Award, 2021

• National Science Foundation (NSF) Graduate Research Fellowship (GRF) recipient, 2021

• Summer Research in Partial Differential Equations Grant recipient, both in 2019 and 2020

• Barry M. Goldwater Scholar, 2020 - 2021

• Roger N. Pedersen Memorial Award recipient, 2019-2020

• Richard A. Moore Scholar, 2018-2019