Asymptotic Behavior of Solutions to the IBVP of the Compressible Navier-Stokes- Korteweg Equations
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题目： Asymptotic Behavior of Solutions to the IBVP of the Compressible Navier-Stokes- Korteweg Equations
报告人： 黎野平 教授 （南通大学）
摘要:In this talk, I am going to present the time-asymptotic behavior of strong solutions to the initial-boundary value problem of the isothermal compressible fluid models of Korteweg type with density-dependent viscosity and capillarity on the half-line . The case when the pressure , the viscosityand the capillarity for the specific volume v(t,x)>0 is considered, where are parameters, and are given positive constants. I focus on the impermeable wall problem where the velocity u(t,x) on the boundary x=0 is zero. If and satisfy some conditions and the initial data have the constant states (v_+, u_+) at infinity with v_+, u_+>0, and have no vacuum and mass concentrations, we prove that the one-dimensional compressible Navier-Stokes-Korteweg system admits a unique global strong solution without vacuum, which tends to the 2-rarefction wave as time goes to infinity. Here both the initial perturbation and the strength of the rarefaction wave can be arbitrarily large. As a special case of the parameters and the constants, the large-time behavior of large solutions to the compressible quantum Navier-Stokes system is also obtained for the first time. Our analysis is based on a new approach to deduce the uniform-in-time positive lower and upper bounds on the specific volume and a subtle large-time stability analysis. This is a joint work with Prof. Chen Zhengzheng.