学术报告

Asymptotic Behavior of Solutions to the IBVP of the Compressible Navier-Stokes- Korteweg Equations

发布人：发布时间： 2021-06-18

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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）

**时间: **2021年6月23日上午9：00

**地点:** 蒙民伟楼1105

**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.

**邀请人：**栗付才 老师