應(yīng)yl7703永利官網(wǎng)王躍循教授邀請，南通大學(xué)理學(xué)院黎野平教授將于2023年5月15日上午舉辦學(xué)術(shù)報(bào)告。

報(bào)告題目：Asymptotic behavior of the solutions towards the rarefaction wave of the 1D compressibleNSK equations

報(bào)告摘要：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 $\mathbb{R}^+$. The case when the pressure $p(v)=v^{-\gamma}$, the viscosity $\mu(v)=\tilde{\mu} v^{-\alpha}$ and the capillarity $\kappa(v)=\tilde{\kappa} v^{-\beta}$ for the specific volume $v(t,x)>0$ is considered, where $\alpha,\beta, \gamma\in\mathbb{R}$ are parameters, and $\tilde{\mu},\tilde{\kappa}$ 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 $\alpha,\beta$ and $\gamma$ 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 $\alpha,\beta$ and the constants $\tilde{\mu},\tilde{\kappa}$, the large-time behavior of large solutions to the compressible quantum Navier-Stokes system is also obtained. 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.

時(shí) 間：5月15日（星期一）09：00-10: 00

地點(diǎn)：理工樓518

歡迎廣大師生光臨!

黎野平教授簡介

黎野平，南通大學(xué)理學(xué)院教授、博士研究生導(dǎo)師、湖北“楚天學(xué)者”特聘教授。先后在湖北大學(xué)、武漢大學(xué)和香港中文大學(xué)獲教育學(xué)學(xué)士學(xué)位、理學(xué)碩士學(xué)位和博士學(xué)位。主要致力于非線性偏微分方程的研究，尤其是來自物理、材料、生物和醫(yī)學(xué)等自然科學(xué)中的各類非線性偏微分方程和非線性耦合方程組。在《Mathematical Models and Methods in Applied Sciences》，《SIAM Journal of Mathematical Analysis》，《Journal of Differential Equations》和《Communications in Mathematical Sciences》等國際、國內(nèi)的重要學(xué)術(shù)期刊雜志上發(fā)表論文90余篇，其中SCI80余篇。同時(shí)，主持完成國家自然科學(xué)基金3項(xiàng)和教育部博士點(diǎn)博導(dǎo)專項(xiàng)、上海市教委創(chuàng)新項(xiàng)目以及江蘇省自然科學(xué)基金等省部級科研項(xiàng)目10余項(xiàng)；現(xiàn)在正主持國家自然科學(xué)基金面上項(xiàng)目1項(xiàng)和參加國家自然科學(xué)基金面上項(xiàng)目2項(xiàng)。

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甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級重點(diǎn)實(shí)驗(yàn)室

yl7703永利官網(wǎng)

萃英學(xué)院

2023年5月12日