Local Existence and Uniqueness of Strong Solution to the Inhomogeneous Primitive Equations with Vacuum

被引：0
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作者：
Xiaoling Hu
Kunzhuo Tong
Xiaojing Xu
机构：
[1] Jiangxi Normal University,School of Mathematics and Statistics, and Jiangxi Provincial Center for Applied Mathematics
[2] Beijing Normal University and Laboratory of Mathematics and Complex Systems,School of Mathematical Sciences
[3] Ministry of Education,undefined
[4] High School Attached to Northeast Normal University,undefined
来源：
Acta Applicandae Mathematicae | 2023年 / 186卷
关键词：
Inhomogeneous primitive equations; Existence; Vacuum;
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摘要：
In this paper, we establish the existence and uniqueness of the local strong solution to the Cauchy problem of the inhomogeneous incompressible primitive equations in a periodic domain. Inspired by the work (J. Li in J. Differ. Equ. 263:6512–6536, 2017), we remove the compatibility condition required in (Q. Jiu and F. Wang in Acta Math. Sci. Ser. B Engl. Ed. 40:1316–1334, 2020), and permit the initial density with vacuum. Meanwhile, we prove the existence of the eigenfunctions to the hydrostatic Stokes operator.
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