Junha Kim

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math.AP2025

Wellposedness of inviscid SQG in the half-plane

In-Jee Jeong, Junha Kim, Hideyuki Miura

We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3, p}$ and $C^{2, I^^{2}}$ for any $…

math.AP2025

On the axially symmetric solutions to the spatially homogeneous Landau equation

Jin Woo Jang, Junha Kim

In this paper, we consider the spatially homogeneous Landau equation, which is a variation of the Boltzmann equation in the grazing collision limit. For the Landau equation for har…

math.AP2024

On well/ill-posedness for the generalized surface quasi-geostrophic equations in HÃ¶lder spaces

Young-Pil Choi, Jinwook Jung, Junha Kim

We establish the well/ill-posedness theories for the inviscid $I^\pm$ -surface quasi-geostrophic ( $I^\pm$ -SQG) equations in HÃ¶lder spaces, where $I^\pm = 0$ and $I^\pm = 1$ correspond to the two…