AI 中文总结
针对三维区域中带压力松弛的粘性Baer-Nunziato系统，研究人员构造了全局耗散测度值解并证明其弱-强唯一性，解决了体积分数消失时的奇异行为等核心难题。
AI 中文摘要
我们在有界三维区域中研究两种正压可压缩流体的粘性单速度Baer-Nunziato系统。与体积分数仅被输运或由代数平衡约束确定的模型不同，该系统的体积分数满足由两相压力差驱动的微分封闭关系。对于任意有限能量初始数据及绝热指数γ±>1，我们构造了时间全局的耗散测度值解，并证明了相对于具有相同初始数据的任意足够正则解的耗散测度值-强唯一性。主要困难在于：体积分数消失时压力松弛源的奇异非连续行为、相关的集中缺陷，以及标准热力学相对能量相对于体积分数缺乏直接强制性。这些困难通过端点截断论证，以及与重正化体积分数方程耦合的增广相对能量得到解决。
英文摘要
We study a viscous one-velocity Baer--Nunziato system for two barotropic compressible fluids in a bounded three-dimensional domain. In contrast with models in which the volume fraction is merely transported or determined by an algebraic equilibrium constraint, it satisfies a differential closure driven by the pressure gap between the phases. For arbitrary finite-energy initial data and adiabatic exponents $γ^\pm>1$, we construct global-in-time dissipative measure-valued solutions and prove dissipative measure-valued--strong uniqueness relative to any sufficiently regular solution with the same initial data. The principal difficulties are the singular and non-continuous behavior of the pressure-relaxation source at vanishing volume fractions, the associated concentration defects, and the lack of direct coercivity of the standard thermodynamic relative energy with respect to the volume fraction. These are resolved by an endpoint cutoff argument and an augmented relative energy coupled to the renormalized volume-fraction equation.
