講座題目：Sharp Interface Limit for Compressible Immiscible Two-Phase Dynamics with Relaxation

講座專家：施小丁教授

講座對(duì)象：基礎(chǔ)數(shù)學(xué)專業(yè)碩士生

講座時(shí)間：2024年5月18日上午10:00-11:00

講座地點(diǎn)：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院3304教室

內(nèi)容摘要：In this talk, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math., 48,1995]) in view of the numerical approximation of conservation laws. Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the  sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system,  here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof.

專家簡(jiǎn)介：施小丁,，北京化工大學(xué)教授,，博士生導(dǎo)師，1996年博士畢業(yè)于中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院,。主要研究領(lǐng)域?yàn)榱黧w力學(xué)方程組的相關(guān)問題,，包括可壓縮Navier-Stokes方程組的波的疊加,、碰撞等大時(shí)間行為；非牛頓不可壓縮Navier-Stokes方程組固液耦合問題和混合邊值問題解的適定性及數(shù)值分析等,。部分成果發(fā)表在數(shù)學(xué)領(lǐng)域的重要雜志Comm. Math. Phys., Indiana Univ. Math. J., SIAM J. Math. Anal., Nonlinearity, J. Differential Equations等,，多次主持和參與國家自然科學(xué)基金項(xiàng)目。