Hyunju Kwon

Research

We interact with fluids every day, yet predicting their flow remains a significant challenge due to a chaotic phenomenon called turbulence. My research focuses on understanding turbulence through the study of partial differential equations (PDEs) that describe fluid behavior, such as the Euler and Navier-Stokes equations. Recently, I have been working on constructing flows that capture the key features of ideal turbulence. I am also interested in exploring the behavior of irregular solutions to fluid equations, owing to their relevance to turbulence and continuation past a potential singularity.


Preprints

  1. The $L^3$-based strong Onsager theorem, arXiv:2305.18509, 2023 (with V. Giri and M. Novack)

Journal articles

  1. A wavelet-inspired $L^3$-based convex integration framework for the Euler equations, Ann. PDE, 2024 (with V. Giri and M. Novack)

  2. The role of the pressure in the regularity theory for the Navier-Stokes equations, J. Differ. Equ., 2023

  3. On non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations, Arch Ration Mech Anal, 2022 (with V. Giri)

  4. Local regularity of weak solutions of the hypodissipative Navier-Stokes equations, J. Func. Anal., 2022 (with W. S. Ożański)

  5. On non-uniqueness of Hölder continuous globally dissipative Euler flows, Anal. PDE, 2022 (with C. De Lellis)

  6. Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations, Comm. Math. Phys., 2021 (with X. Cheng and D. Li)

  7. On bifurcation of self-similar solutions of the stationary Navier-Stokes equations, Commun Math Sci., 2021 (with T-P. Tsai)

  8. Strong ill-posedness of logarithmically regularized 2D Euler equations in the critical Sobolev space, J. Func. Anal., 2020

  9. Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation, Comm. Math. Phys., 2020 (with T-P. Tsai)

Lecture notes

  1. Instability and nonuniqueness for the 2d Euler equations in vorticity form, after M. Vishik, Ann. Math. Stud., 2024
    (with D. Albritton, E. Brué, M. Colombo, C. De Lellis, V. Giri, and M. Janisch)