叶蕊萍,孔春香

• 1:延安大学数学与计算机科学学院

摘要(Abstract)：

本文中研究一类粘性系数为常数和热传导系数依赖于温度的非等熵可压缩Navier-Stokes/Allen-Cahn系统。在大初始值条件下，将系统转化为拉格朗日坐标下的初边值问题，构造了适当的能量函数，以此为条件，运用基本能量方法，结合Gronwall不等式、分部积分和嵌入定理等技巧，系统性地控制了密度、速度、温度与相变量的各阶导数，得出温度和密度有正的上下界。通过建立全局先验估计，完成了该系统强解存在性的证明。

关键词(KeyWords)： Navier-Stokes/Allen-Cahn方程;热传导系数依赖于温度;全局解

Abstract:

Keywords:

基金项目(Foundation): 陕西省科技计划项目(2021JM-419);; 延安大学2023年大学生创新训练项目(D2023051)资助

作者(Author): 叶蕊萍,孔春香

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