arXiv subjects

Sangwook Tae

Publications and source records attributed to Sangwook Tae.

3 recordsLinked to original sources

arXiv2026

Well-posedness for Vlasov--Poisson on Low Regularity $H^{s,p}$ Spaces in All Dimensions

We consider the Vlasov--Poisson equation on $\mathbb{R}^d \times \mathbb{R}^d$ for any dimension. For initial distribution $f_{0}$ having compact support in $v$ and belonging to $H^{s,p}(\mathbb{R}^d \times \mathbb{R}^d)$, we prove local well-posedness for $s>\frac{d}{p}-\frac{1}{2p}$ and $p\in[2, \infty)$. We proved this by using two main ingredients, which is the averaging property for the density $\rho$ and the Schauder-Tychonoff fixed point theorem. It seems like this is the first application of the Schauder-Tychonoff fixed point theorem in showing existence of solution for evolutionary PDEs.

math.AP↗

arXiv2025

Low regularity Sobolev well-posedness for Vlasov--Poisson

We consider the Vlasov--Poisson equation on $\mathbb{R}^n \times \mathbb{R}^n$ with $n \ge 3$. We prove local well-posedness in $H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ with $s> n/2-1/4$, for initial distribution $f_{0} \in H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ having compact support in $v$. In particular, data not belonging to $L^p(\mathbb{R}^n \times \mathbb{R}^n)$ for large $p$ are allowed.

math.AP↗

arXiv2024

Twisting in One Dimensional Periodic Vlasov-Poisson System

We prove that twisting and filamentation occur near a family of stable steady states for one dimensional periodic Vlasov-Poisson system, describing the electron dynamics under a fixed ion background. More precisely, we establish the growth in time of the L1 norm of the gradient for the electron distribution function and the corresponding flow map in the phase space. To support this result, we prove existence results of stable steady states for a class of ion densities on the torus.

math.AP↗