论文标题
全球强的解决方案，用于与1-D中温度相关的热传导性的热力学压缩弥散界面模型
Global Strong Solution to a Thermodynamic Compressible Diffuse Interface Model with Temperature Dependent Heat-conductivity in 1-D
论文作者
论文摘要
在本文中，我们研究了非分离性可压缩的Navier-Stokes/Allen-CAHN系统的良好性，其热传导性与温度的正功率成正比。该系统描述了两相不混溶的热传导粘性压缩混合物的流动。由于流体中的密度变化，允许这些相位缩小或生长，并将其转运与电流结合在一起。我们在1-D中建立了该系统的强溶液的全球存在和独特性，这意味着在有限的时间内将开发相位分离，真空，冲击波，质量或热量或相位浓度，尽管两相不混可能的流动的运动具有较大的振荡，并且在流体动力学和相位领域效应之间的相互作用很复杂。我们的结果可以被视为对Kazhikhov-Shelukhin的结果的自然概括（[[[Kazhikhov-Shelukhin。J.Appl。Math。Math。Math。41（1977）]），用于可压缩的单相流量，具有恒定的热电导率，可对非异常可压缩的不可压缩的两相流动，并带有非月份和非一个不适的耐热性。
In this paper, we investigate the wellposedness of the non-isentropic compressible Navier-Stokes/Allen-Cahn system with the heat-conductivity proportional to a positive power of the temperature. This system describes the flow of a two-phase immiscible heat-conducting viscous compressible mixture. The phases are allowed to shrink or grow due to changes of density in the fluid and incorporates their transport with the current. We established the global existence and uniqueness of strong solutions for this system in 1-D, which means no phase separation, vacuum, shock wave, mass or heat or phase concentration will be developed in finite time, although the motion of the two-phase immiscible flow has large oscillations and the interaction between the hydrodynamic and phase-field effects is complex. Our result can be regarded as a natural generalization of the Kazhikhov-Shelukhin's result ([Kazhikhov-Shelukhin. J. Appl. Math. Mech. 41 (1977)]) for the compressible single-phase flow with constant heat conductivity to the non-isentropic compressible immiscible two-phase flow with degenerate and nonlinear heat conductivity.
