The present paper deals with the Cauchy problem of a compressible generic two-fluid model with capillarity effects in any dimension $N\geq2$. We first study the unique global solvability of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. Due to the presence of the capillary terms, we exploit the parabolic properties of the linearized system for all frequencies which enables us to apply contraction mapping principle to show 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 optimal time decay rates for the constructed global solutions.

中文翻译：

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具有毛细作用效应的多维可压缩通用二流体模型的独特全局可解性和最佳时间衰减率*

本论文涉及在任何维度 $N\geq2$ 中具有毛细作用效应的可压缩通用双流体模型的柯西问题。我们首先研究模型在具有关键规律性指数的空间中独特的全局可解性，与相关方程的缩放相关。由于毛细项的存在，我们针对所有频率利用线性化系统的抛物线特性，这使我们能够应用收缩映射原理来显示接近稳定平衡状态的强解的独特全局可解性。此外，在仅涉及数据低频的温和附加衰减假设下，我们为构建的全局解决方案建立了最佳时间衰减率。