Global small solution and optimal decay rate for the Korteweg system in Besov spaces

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发表日期：

2025年6月8日

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Jinlu Li,
Yanghai Yu,
Weipeng Zhu

摘要

In this paper, we consider the Cauchy problem for the Korteweg system with the general pressure in dimension $d\ge 2$ $d \geq 2$ and establish the global well-posedness of strong solution for the small initial data in $L^p$ $L^{p}$ type critical Besov spaces. Furthermore, we obtain the optimal decay rate of solution to the Korteweg system in $L^2$ $L^{2}$ type Besov spaces.