8 papers
Asymptotic stability of viscous shock for the outflow problem of 3D Navier-Stokes system
Moon-Jin Kang, Hyeonseop Kim, Hobin Lee
We establish the asymptotic stability of planar viscous shock waves for the outflow problem of the three-dimensional barotropic compressible Navier--Stokes equations in a half-spac…
Long-time dynamics toward a generic composite wave for the inflow problem of the Navier--Stokes--Fourier system
Xushan Huang, Moon-Jin Kang, Hobin Lee +1
We study the time-asymptotic stability of solutions to the inflow problem for the one-dimensional Navier--Stokes--Fourier system on the half-line. We consider the most generic wave…
Stability of viscous shock for the Navier-Stokes-Fourier system: outflow and impermeable wall problems
Xushan Huang, Hobin Lee, HyeonSeop Oh
We investigate the time-asymptotic stability of solutions to the one-dimensional Navier-Stokes-Fourier system in the half-space, focusing on the outflow and impermeable wall proble…
Time-asymptotic stability of composite wave of viscous shocks and viscous contact wave for Navier-Stokes-Fourier equations
Xushan Huang, Hobin Lee
We investigate the nonlinear time-asymptotic stability of the composite wave consisting of two viscous shocks and a viscous contact discontinuity for the one-dimensional compressib…
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 toward composite wave of shocks for 3D barotropic navier-stokes system
Moon-Jin Kang, Hobin Lee
We consider the barotropic Navier-Stokes system in three space dimensions with periodic boundary condition in the transversal direction. We show the long-time behavior of the 3D ba…
Asymptotic behavior toward viscous shock for impermeable wall and inflow problem of barotropic Navier-Stokes equations
Xushan Huang, Moon-Jin Kang, Jeongho Kim +1
We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider…
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…