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math.AP2026
Existence and uniqueness of viscous-dispersive shock profiles for the Navier-Stokes-Fourier-Korteweg system
Sungho Han
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…
math.AP2026
Large-Time Behavior towards Composite Waves of Degenerate Shock and Rarefaction Wave for Modified KdV-Burgers Equation
Namhyun Eun, Sungho Han, Jeongho Kim
In this paper, we study the modified Korteweg-de Vries-Burgers (mKdVB) equation \[u_t + (u^3)_x = μu_{xx} - κu_{xxx}\] with and . Since the flux is non-convex, the (invi…
math.AP2026
Time-asymptotic stability of viscous shocks for the outflow problem of one-dimensional compressible fluids of Korteweg type
Sungho Han, Jeongho Kim, HyeonSeop Oh
We study the time-asymptotic stability of viscous-dispersive shock waves for the outflow problem of the barotropic Navier--Stokes--Korteweg equations, which describe viscous fluids…