8 papers
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…
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…
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…
Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type
Sungho Han, Jeongho Kim
We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg type, called the Navier-Stokes-K…
Convergence to Superposition of Boundary Layer, Rarefaction and Shock for the Inflow Problem of the 1D Navier--Stokes Equations
Sungho Han, Moon-Jin Kang, Jeongho Kim +2
We establish the asymptotic stability of solutions to the inflow problem for the one-dimensional barotropic Navier--Stokes equations in half space. When the boundary value is locat…
The method of -contraction with shifts used for long-time behavior toward viscous shock
Sungho Han, Moon-Jin Kang, Hobin Lee
We revisit the method of -contraction with shifts used for long-time behavior of barotropic Navier-Stokes flows perturbed from a Riemann shock. For the usage of the method of $a…
Long-time behavior towards viscous-dispersive shock for Navier-Stokes equations of Korteweg type
Sungho Han, Moon-Jin Kang, Jeongho Kim +1
We consider the so-called Naiver-Stokes-Korteweg(NSK) equations for the dynamics of compressible barotropic viscous fluids with internal capillarity. We handle the time-asymptotic…
Large-time behavior of composite waves of viscous shocks for the barotropic Navier-Stokes equations
Sungho Han, Moon-Jin Kang, Jeongho Kim
We study the large-time behavior of the 1D barotropic Navier-Stokes flow perturbed from Riemann data generating a composition of two shock waves with small amplitudes. We prove tha…