Speaker：Yeping Li（Nantong University）

Time：2022-05-13, 10:15

Venue：Tencent Meeting ID：8226760016（No Password）

Abstract:

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 R^+. The case when the pressure p(v)=v^(-γ), the viscosity μ(v)= μ᷉ v^(-α) and the capillarity κ(v)=κ᷉ v^(-β ) for the specific volume v(t,x)>0 is considered, where α, β, γ∈R are parameters, and μ᷉, κ᷉ 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 α, β and γ 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 α, β and the constants μ᷉, κ᷉, 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.