论文标题
最大规律性及其在$ l^{p} $中的多维非保守粘性可压缩的两流体型模型中的应用
The maximal regularity and its application to a multi-dimensional non-conservative viscous compressible two-fluid model with capillarity effects in $L^{ p}$-type framework
论文作者
论文摘要
本文是工作\ cite {xc}的延续，致力于将其扩展到与能量空间无关的关键功能框架。我们采用具有毛细血管效应的非保守粘性可压缩两流体模型的特殊耗散结构，我们首先利用所有频率中相应线性化系统的最大规律性估计值，其表现为热方程。然后，当初始数据与合适的$ l^{p} $ - 键入besov norms的意义上时，我们为多维模型构建了全局良好性。结果，这使我们能够在带有负定性索引的BESOV空间的框架中工作，当初始数据在物理维度上高度振荡时，这一事实尤其重要，$ n = 2，3 $。此外，基于傅立叶空间中精制的时间加权不平等，我们还建立了在温和的额外衰变假设下为构造的全球溶液的最佳时间衰减率，仅涉及初始数据的低频。
The present paper is the continuation of work \cite{XC}, devoted to extending it to a critical functional framework which is not related to the energy space. Employing the special dissipative structure of the non-conservative viscous compressible two-fluid model with capillarity effects, we first exploit the maximal regularity estimates for the corresponding linearized system in all frequencies which behaves like the heat equation. Then we construct the global well-posedness for the multi-dimensional model when the initial data are close to a stable equilibrium state in the sense of suitable $L^{ p}$-type Besov norms. As a consequence, this allows us to work in the framework of Besov space with negative regularity indices and this fact is particularly important when the initial data are large highly oscillating in physical dimensions $N= 2, 3$. Furthermore, based on a refined time weighted inequalities in the Fourier spaces, we also establish optimal time decay rates for the constructed global solutions under a mild additional decay assumption involving only the low frequencies of the initial data.
