Author

Jeongho Kim

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Preprint Oct 2026

Time-asymptotic stability of generic Riemann solutions for viscous-dispersive heat-conducting compressible fluids

We establish the time-asymptotic stability of generic Riemann solutions for the one-dimensional Navier-Stokes-Fourier-Korteweg (NSFK) system, which describes the dynamics of viscous, heat-conducting, compressible fluids with internal capillarity. We prove that, for the adiabatic exponent $\gamma\in(1,2]$, the solution...

S. Han, Jeongho Kim · 0 citations

Preprint Sep 2026

Large-Time Behavior towards Composite Waves of Degenerate Shock and Rarefaction Wave for Modified KdV-Burgers Equation

In this paper, we study the modified Korteweg-de Vries-Burgers (mKdVB) equation \[u_t + (u^3)_x = \mu u_{xx} - \kappa u_{xxx}\] with $\mu>0$ and $\kappa>0$. Since the flux is non-convex, the (inviscid) Riemann problem may be solved by a composite wave of a degenerate Oleinik shock and a rarefaction wave. We prove the g...

Namhyun Eun, S. Han, Jeongho Kim · 2 citations

Preprint Aug 2026

Time-Asymptotic Stability of the Stationary Solution to the Impermeable Wall Problem for the radially Symmetric Navier-Stokes-Korteweg Equations

We study the asymptotic behavior of the initial-boundary value problem for the radially symmetric Navier--Stokes--Korteweg (NSK) equations defined on the exterior domain $\Omega = \{x\in\R^n~|~|x|>1\}$. In particular, we consider the impermeable wall problem, where the velocity at the boundary $\{x\in\R^n~|~|x|=1\}$ is...

Jeongho Kim · 0 citations