GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

doi:10.1007/s10473-022-0207-8

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 521-539.doi: 10.1007/s10473-022-0207-8

GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

王梅¹, 李自来², 郭真华³

1. School of Sciences, Xi'an University of Technology, Xi'an 710048, China;
2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;
3. School of Mathematics and Information Science, Guangxi University, Nanning 530004, China

收稿日期:2020-03-24 修回日期:2021-02-17 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Mei WANG,E-mail:wangmei0439@163.com E-mail:wangmei0439@163.com
作者简介:Zilai LI,E-mail:lizilai0917@163.com;Zhenhua GUO,E-mail:zhenhua.guo.math@gmail.com
基金资助:
This paper is supported by NNSFC (11701443, 11901444, 11931013) and Natural Science Basic Research Plan in Shaanxi Province of China (2019JQ-870).

GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

Mei WANG¹, Zilai LI², Zhenhua GUO³

1. School of Sciences, Xi'an University of Technology, Xi'an 710048, China;
2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;
3. School of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received:2020-03-24 Revised:2021-02-17 Online:2022-04-25 Published:2022-04-22
Supported by:
This paper is supported by NNSFC (11701443, 11901444, 11931013) and Natural Science Basic Research Plan in Shaanxi Province of China (2019JQ-870).

摘要/Abstract

摘要： In this paper, we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosity μ is a positive constant and the bulk viscosity is λ(ρ) = ρ^β with β > 2, which is a situation that was first introduced by Vaigant and Kazhikhov in [1]. The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω = {(r, z)|r = √x² + y², (x, y, z) ∈ R³, r ∈ I ⊂ (0, +∞), −∞ < z < +∞} is obtained. Here the initial density keeps a non-vacuum state p > 0 when z → ±∞. Our results also show that the solution will not develop the vacuum state in any finite time, provided that the initial density is uniformly away from the vacuum.

关键词: Navier-Stokes equations, axisymmetric, density-dependent, classical solution

Abstract: In this paper, we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosity μ is a positive constant and the bulk viscosity is λ(ρ) = ρ^β with β > 2, which is a situation that was first introduced by Vaigant and Kazhikhov in [1]. The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω = {(r, z)|r = √x² + y², (x, y, z) ∈ R³, r ∈ I ⊂ (0, +∞), −∞ < z < +∞} is obtained. Here the initial density keeps a non-vacuum state p > 0 when z → ±∞. Our results also show that the solution will not develop the vacuum state in any finite time, provided that the initial density is uniformly away from the vacuum.

Key words: Navier-Stokes equations, axisymmetric, density-dependent, classical solution

中图分类号:

35Q30

王梅, 李自来, 郭真华. GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2022, 42(2): 521-539.

Mei WANG, Zilai LI, Zhenhua GUO. GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY[J]. Acta mathematica scientia,Series B, 2022, 42(2): 521-539.

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GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

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