A Generalized Typicality for Abstract Alphabets
Junekey Jeon. 2014. "A Generalized Typicality for Abstract Alphabets." 2014 IEEE International Symposium on Information Theory (ISIT), 2649-2653
Posts by Collection
publications
A Bayesian sensor fusion scheme for attitude tracking
Junekey Jeon, Hwa-Suk Kim, Woo-Sug Jung and Sun-Joong Kim. 2017. "A Bayesian sensor fusion scheme for attitude tracking." 2017 19th International Conference on Advanced Communication Technology (ICACT)
Spectral clustering with brainstorming process for multi-view data
Jeong-Woo Son, Junekey Jeon, Alex Lee and Sun-Joong Kim. 2017. "Spectral clustering with brainstorming process for multi-view data." Proceedings of the AAAI Conference on Artificial Intelligence, 2548–2554
On evolution of corner-like gSQG patches
Junekey Jeon and In-Jee Jeong. "On Evolution of Corner-Like gSQG Patches." J. Math. Fluid Mech. 25, 35 (2023)
An Improved Regularity Criterion and Absence of Splash-like Singularities for g-SQG Patches
Junekey Jeon and Andrej Zlatoš. "An Improved Regularity Criterion and Absence of Splash-like Singularities for g-SQG Patches." Anal. PDE 17, 3 (2024)
talks
An Improved Regularity Criterion and Absence of Splash-like Singularities for g-SQG Patches
We prove that splash-like singularities cannot occur for sufficiently regular patch solutions to the generalized surface quasi-geostrophic equation on the plane or half-plane with parameter $\alpha \le 1/4$. This includes potential touches of more than two patch boundary segments in the same location, an eventuality that has not been excluded previously and presents nontrivial complications (in fact, if we do a priori exclude it, then our results extend to all $\alpha \in (0,1)$). As a corollary, we obtain an improved global regularity criterion for H3 patch solutions when $\alpha \le 1/4$, namely that finite time singularities cannot occur while the H3 norms of patch boundaries remain bounded.
Abstract Level-Set Dynamics of gSQG Equation
We develop an abstract measure-theoretic notion of solutions to gSQG equation based on the dynamics of level-sets of solutions, and prove an $H^{2}$ local-wellposedness result in this setting using a sequence of regularized contour equations.
teaching
MATH 110. Introduction to Partial Differential Equations
Undergraduate course, University of California San Diego, 2019
MATH 140B. Foundations of Real Analysis II
Undergraduate course, University of California San Diego, 2020
MATH 140C. Foundations of Real Analysis III
Undergraduate course, University of California San Diego, 2020
MATH 144. Introduction to Fourier Analysis
Undergraduate course, University of California San Diego, 2020
MATH 20D. Introduction to Differential Equations
Undergraduate course, University of California San Diego, 2020
MATH 130. Differential Equations and Dynamical Systems
Undergraduate course, University of California San Diego, 2021
MATH 20D. Introduction to Differential Equations
Undergraduate course, University of California San Diego, 2021
MATH 142A. Introduction to Analysis I
Undergraduate course, University of California San Diego, 2021
MATH 20D. Introduction to Differential Equations
Undergraduate course, University of California San Diego, 2022
MATH 10B. Calculus II
Undergraduate course, University of California San Diego, 2022
MATH 144. Introduction to Fourier Analysis
Undergraduate course, University of California San Diego, 2022
MATH 140B. Foundations of Real Analysis II
Undergraduate course, University of California San Diego, 2023
MATH 140C. Foundations of Real Analysis III
Undergraduate course, University of California San Diego, 2023
MATH 240C. Real Analysis III
Graduate course, University of California San Diego, 2023
MATH 20D. Introduction to Differential Equations
Undergraduate course, University of California San Diego, 2023
MATH 20E. Vector Calculus
Undergraduate course, University of California San Diego, 2024
MATH 148. Analysis of Partial Differential Equations
Undergraduate course, University of California San Diego, 2024