论文标题
非异类压缩的Navier-Stokes/Allen-CAHN系统的库奇问题具有退化热导率
The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity
论文作者
论文摘要
本文讨论了1-d中非异源性压缩的Navier-Stokes/Allen-CAHN系统，具有退化热传导性$κ（θ）= \tildeκθ^β$在1-D中。该系统被广泛用于描述数值模拟中不混溶的两相流动的运动。使用$ H^1 $的密度，温度，速度和相位字段的$ H^2 $初始数据的初始数据确定了强大解决方案的良好性。结果表明，在整个空间中的任何有限时间都将开发相场，真空，冲击波，质量或热浓度的不连续性。从流体动力学的角度来看，这意味着无论流体动力学和相位场效应之间的相互作用多么复杂，都不会发生相分离，但是相位跃迁是可能的。
The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn system with degenerate heat-conductivity $κ(θ)=\tildeκθ^β$ in 1-d is discussed in this paper. This system is widely used to describe the motion of immiscible two-phase flow in numerical simulation. The wellposedness for strong solution of this problem is established with the $H^1$ initial data for density, temperature, velocity, and the $H^2$ initial data for phase field. The result shows that no discontinuity of the phase field, vacuum, shock wave, mass or heat concentration will be developed at any finite time in the whole space. From the hydrodynamic point of view, this means that no matter how complex the interaction between the hydrodynamic and phase-field effects, phase separation will not occur, but the phase transition is possible.
