Theme: Asymptotic Behavior of Solutions to the IBVP of the Compressible Navier-Stokes -Korteweg Equations
Time：10:30am, 23rd, July, 2021
Place：Room 213, Mathematics Building, Nanhu Campus
Lecturer：Professor Li Yeping
In this talk, I am going to presnet 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 viscosity and 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.
Information of the lecturer:
Li Yeping, Professor and Doctoral Supervisor of School of Sciences, Nantong University, and distinguished professor of “Chutian Scholar” of Hubei Province. He received his B.Ed, M.Sc and Ph.D. degrees from Hubei University, Wuhan University and the Chinese University of Hong Kong. He is mainly engaged in the research of nonlinear partial differential equations, especially various types of nonlinear partial differential equations and nonlinear coupled equation systems in natural sciences such as physics, materials, biology and medicine. He has published more than 90 papers, including more than 70 SCI papers, in international and domestic academic journals, such asMathematical Models and Methods in Applied Sciences, SIAM Journal of Mathematical Analysis, Journal of Differential Equations. And he has presided over and completed 3 projects of the National Natural Science Foundation of China and 4 projects of the Ministry of Education and Shanghai Natural Science Foundation of China. He is now participating in 2 projects of the National Natural Science Foundation of China.