A Strong Solution of Navier-Stokes Equations with a Rotation Effect for Isentropic Compressible Fluids

被引:0
作者
Tuowei Chen
Yongqian Zhang
机构
[1] Fudan University,School of Mathematical Sciences
来源
Acta Mathematica Scientia | 2021年 / 41卷
关键词
compressible Navier-Stokes equations; rotating obstacle; exterior domain; vacuum; strong solutions; 35Q30; 76N10; 76N15; 76U05;
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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.
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页码:1579 / 1605
页数:26
相关论文
共 46 条
[1]  
Agmon S(1964)Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II Comm Pure Appl Math 17 35-92
[2]  
Douglis A(2019)Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball J Differential Equations 267 7047-7063
[3]  
Nirenberg L(2004)Unique solvability of the initial boundary value problems for compressible viscous fluids J Math Pures Appl (9) 83 243-275
[4]  
Bian D(2003)Strong solutions of the Navier-Stokes equations for isentropic compressible fluids J Differential Equations 190 504-523
[5]  
Li J(2016)Blowup criterion for the compressible fluid-particle interaction model in 3D with vacuum Acta Mathematica Scientia 36B 1030-1048
[6]  
Cho Y(2015)A linearized model for compressible flow past a rotating obstacle: analysis via modified Bochner-Riesz multipliers Z Anal Anwend 34 285-308
[7]  
Choe H J(2006)-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle J Reine Angew Math 596 45-62
[8]  
Kim H(2014)The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: the nonautonomous case J Reine Angew Math 694 1-26
[9]  
Choe H J(1999)An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle Arch Ration Mech Anal 150 307-348
[10]  
Kim H(1999)The Stokes operator with rotation effect in exterior domains Analysis (Munich) 19 51-67