Weak-strong uniqueness principle for the two-fluid compressible viscous systems
数学专题报告
报告题目(Title)：Weak-strong uniqueness principle for the two-fluid compressible viscous systems
报告人(Speaker)：Prof. Ewelina Zatorska（University of Warwick, UK）
地点(Place)：Zoom Meeting ID: 840 012 91050 | Password: 123456
时间(Time)：2026年10月8日（周四）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
I will discuss two recent results on the weak-strong uniqueness principle for two-phase compressible viscous fluid systems with two different closure laws: algebraic and differential. For the algebraic closure, starting from the already available weak solutions and local-in-time strong solutions, we show that a suitable convexification of a parametrised, piecewise-defined relative entropy functional allows us to identify the two solutions on the lifespan of the strong solution. For the differential closure, corresponding to the Baer-Nunziato system, we first construct dissipative measure-valued solutions and compare them with the corresponding local-in-time strong solutions. We show that augmenting the relative entropy by a pressure-gap dissipation term arising from the closure relation allows us to establish the measure-valued-strong uniqueness principle. The result holds for arbitrary finite-energy initial data and adiabatic exponents γ^± > 1. The main difficulties arise from the singular and discontinuous behaviour of the pressure-relaxation source as the volume fractions vanish, the associated concentration effects, and the lack of direct coercivity of the standard thermodynamic relative energy with respect to the volume fraction. These difficulties are overcome by an endpoint cutoff argument combined with a reversal of the usual order of approximation. As a byproduct, the so-called “no-pure-phase” restriction on the initial data can be removed.
