A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

doi:10.1007/s10473-021-0511-8

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1579-1605.doi: 10.1007/s10473-021-0511-8

A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

陈拓炜, 张永前

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

收稿日期:2020-01-19 修回日期:2021-05-09 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Tuowei CHEN E-mail:16110180003@fudan.edu.cn
作者简介:Yongqian ZHANG,Email:yongqianz@fudan.edu.cn
基金资助:
This work was partially supported by NSFC (11421061), and by National Science Foundation of Shanghai (15ZR1403900).

A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

Tuowei CHEN, Yongqian ZHANG

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received:2020-01-19 Revised:2021-05-09 Online:2021-10-25 Published:2021-10-21
Contact: Tuowei CHEN E-mail:16110180003@fudan.edu.cn
Supported by:
This work was partially supported by NSFC (11421061), and by National Science Foundation of Shanghai (15ZR1403900).

摘要/Abstract

摘要： We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle, with initial density having a compact support. By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions, we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain. We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains, and derive some uniform bounds of higher order norms, which are independent of the size of the bounded domains. Then we prove the local existence of unique strong solution of the problem in the exterior domain, provided that the initial data satisfy a natural compatibility condition.

关键词: compressible Navier-Stokes equations, rotating obstacle, exterior domain, vacuum, strong solutions

Abstract: We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle, with initial density having a compact support. By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions, we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain. We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains, and derive some uniform bounds of higher order norms, which are independent of the size of the bounded domains. Then we prove the local existence of unique strong solution of the problem in the exterior domain, provided that the initial data satisfy a natural compatibility condition.

Key words: compressible Navier-Stokes equations, rotating obstacle, exterior domain, vacuum, strong solutions

中图分类号:

35Q30

陈拓炜, 张永前. A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS[J]. 数学物理学报(英文版), 2021, 41(5): 1579-1605.

Tuowei CHEN, Yongqian ZHANG. A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1579-1605.

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A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

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