论文标题
关于多维非保守粘性可压缩的两流体系统的强溶液的适合性和衰减速率
On the well-posedness and decay rates of strong solutions to a multi-dimensional non-conservative viscous compressible two-fluid system
论文作者
论文摘要
本文涉及多维非保守粘性可压缩两流体系统的库奇问题。我们首先在相关方程的尺度上研究了具有关键规律性指数的空间中模型的适当性。在尽可能接近物理能量空间的功能设置中，我们证明了靠近稳定平衡状态的强溶液的独特全局溶解性。此外，在仅涉及数据低频的轻度额外衰减假设下，我们确定了构造的全球溶液的时间衰减率。证明依赖于将傅立叶分析应用于复杂的抛物线纤维填充系统，以及精致的时间加权不平等。
The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. In the functional setting as close as possible to the physical energy spaces, we prove the unique global solvability of strong solutions close to a stable equilibrium state. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we establish the time decay rates for the constructed global solutions. The proof relies on an application of Fourier analysis to a complicated parabolic-hyperbolic system, and on a refined time-weighted inequality.
