arXiv subjects

Jihoi Kim

Publications and source records attributed to Jihoi Kim.

3 recordsLinked to original sources

arXiv2026

On smooth self similar solution to compressible Euler equation with physical vacuum

We consider the barotropic Euler equations in dimension $d > 1$ with decaying density at spatial infinity. The phase portrait of the nonlinear ODE governing the equation for spherically symmetric self-similar solutions has been introduced in the pioneering work of Guderley. The existence of smooth decaying solutions through the sonic line has been obtained in the work (F. Merle et al., 2022) in a suitable range of parameters. We work in this paper in a different range of parameters and show the existence of holosphere like solutions which are smooth through the sonic line, but display vanishing density at a sphere.

math.AP↗

arXiv2024

Self-similar blow up for energy supercritical semilinear wave equation

We analyse the energy supercritical semilinear wave equation $$Φ_{tt}-ΔΦ-|Φ|^{p-1}Φ=0$$ in $\mathbb R^d$ space. We first prove in a suitable regime of parameters the existence of a countable family of self similar profiles which bifurcate from the soliton solution. We then prove the non radial finite codimensional stability of these profiles by adapting the functional setting of arXiv:1912.11005.

math.AP↗

arXiv2024

Magnetic response of twisted bilayer graphene

In this article, we analyse the Bistritzer--MacDonald (BM) model (also known as the continuum model) of twisted bilayer graphene (TBG) with an additional external magnetic field. We provide an explicit semiclassical asymptotic expansion of the density of states (DOS) in the limit of strong magnetic fields. The explicit expansion of the DOS enables us to study magnetic response properties such as magnetic oscillations which includes Shubnikov-de Haas and de Haas-van Alphen oscillations as well as the integer quantum Hall effect. In particular, we elucidate the role played by different types of interlayer tunnelings ($AA^{\prime}$/$BB^{\prime}$ vs. $AB^{\prime}$/$BA^{\prime}$) in the study of the DOS, and magnetic properties.

math-ph↗