EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

doi:10.1007/s10473-025-0612-x

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (6): 2591-2606.doi: 10.1007/s10473-025-0612-x

EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

Yi WANG^1,2,*, Yongfu YANG³, Qiuyang YU^4,5

1. State Key Laboratory of Mathematical Sciences and Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. School of Mathematics, Hohai University, Nanjing 211100, China;
4. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
5. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2025-03-24 修回日期:2025-04-16 出版日期:2025-11-25 发布日期:2025-11-14

EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

Yi WANG^1,2,*, Yongfu YANG³, Qiuyang YU^4,5

1. State Key Laboratory of Mathematical Sciences and Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. School of Mathematics, Hohai University, Nanjing 211100, China;
4. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
5. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2025-03-24 Revised:2025-04-16 Online:2025-11-25 Published:2025-11-14
Contact: ^*Yi WANG, E-mail: wangyi@amss.ac.cn
About author:Yongfu YANG, E-mail: yyang@hhu.edu.cn; Qiuyang YU, E-mail: yuqiuyang@amss.ac.cn
Supported by:
NSFC (12171459, 12288201, 12090014, 12421001) and CAS Project for Young Scientists in Basic Research (YSBR-031).

摘要/Abstract

摘要： We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional (1D) full compressible Navier-Stokes equations on a half line $\mathbb{R}_+$. Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results, the delicate global phase plane analysis, based on the qualitative theory of ODEs, is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic, transonic, and subsonic regions, respectively, which completely answers the existence/non-existence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.

关键词: compressible Navier-Stokes equations, inow problem, large-amplitude bound-ary layer solutions

Abstract: We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional (1D) full compressible Navier-Stokes equations on a half line $\mathbb{R}_+$. Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results, the delicate global phase plane analysis, based on the qualitative theory of ODEs, is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic, transonic, and subsonic regions, respectively, which completely answers the existence/non-existence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.

Key words: compressible Navier-Stokes equations, inow problem, large-amplitude bound-ary layer solutions

中图分类号:

76N06

Yi WANG, Yongfu YANG, Qiuyang YU. EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 2025, 45(6): 2591-2606.

Yi WANG, Yongfu YANG, Qiuyang YU. EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia,Series B, 2025, 45(6): 2591-2606.

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EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

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