Author

S. Han

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Preprint Oct 2026

Existence and uniqueness of viscous-dispersive shock profiles for the Navier-Stokes-Fourier-Korteweg system

We establish the existence and uniqueness, up to translation, of monotone viscous-dispersive shock profiles for the one-dimensional Navier-Stokes-Fourier-Korteweg system, provided the two end states satisfy the Rankine-Hugoniot and Lax entropy conditions and the shock strength is small. Taking the shock strength as a s...

S. Han · 0 citations

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