The 32nd KMGS will be held on April 25th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Sungho Han from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.
Slot (AM 11:50~PM 12:30)
[Speaker] 한성호 (Sungho Han) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 강문진, Moon-Jin Kang
[Title] Long-time behavior of viscous-dispersive shock for the Navier-Stokes-Korteweg equations
[Discipline] Analysis
[Abstract]
We consider the Naiver-Stokes-Korteweg(NSK) equations for the dynamics of compressible barotropic viscous fluids with internal capillarity. We handle the time-asymptotic stability in 1D of the viscous-dispersive shock wave that is a traveling wave solution to NSK as a viscous-dispersive counterpart of a Riemann shock. More precisely, we prove that when the prescribed far-field states of NSK are connected by a single Hugoniot curve, then solutions of NSK tend to the viscous-dispersive shock wave as time goes to infinity. To obtain the convergence, we extend the theory of a-contraction with shifts, used for the Navier-Stokes equations, to the NSK system. The main difficulty in analysis for NSK is due to the third-order derivative terms of the specific volume in the momentum equation. To resolve the problem, we introduce an auxiliary variable that is equivalent to the derivative of the specific volume.
[Language] Korean but English if it is requested