19 citations · 38 across the 9 of their papers we have counts for
10 papers
Weighted singular vectors in common-base self-similar sets
Taehyeong Kim, Jaemin Park
We prove a lower bound for the Hausdorff dimension of weighted totally irrational singular vectors in affine-spanning common-base integral self-similar sets satisfying the open set…
Quasiperiodic solutions of the generalized SQG equation
Javier Gómez-Serrano, Alexandru D. Ionescu, Jaemin Park
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an e…
Circular Coordinates for Density-Robust Analysis
Taejin Paik, Jaemin Park
Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordina…
Atlas flow : compatible local structures on the manifold
Taejin Paik, Jaemin Park, Jung Ho Park
In this paper, we focus on the intersections of a manifold's local structures to analyze the global structure of a manifold. We obtain local regions on data manifolds such as the l…
On a lower bound of Hausdorff dimension of weighted singular vectors
Taehyeong Kim, Jaemin Park
Let be a -tuple of positive real numbers such that and . A -dimensional vector $x=(x_1,\dots,x_d)\in\mathbb{R}^d…
Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy
Javier Gómez-Serrano, Jaemin Park, Jia Shi
In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler equations with compact support but non-concentrated around one or several points. O…
Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via…
Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity , such that it has positive vo…
Quantitative estimates for uniformly-rotating vortex patches
Jaemin Park
In this paper, we derive some quantitative estimates for uniformly-rotating vortex patches. We prove that if a non-radial simply-connected patch is uniformly-rotating with smal…
Symmetry in stationary and uniformly-rotating solutions of active scalar equations
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we study the radial symmetry properties of stationary and uniformly-rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch s…