التفاصيل البيبلوغرافية
| العنوان: |
Stability and related zero viscosity limit of steady plane Poiseuille-Couette flows with no-slip boundary condition. |
| المؤلفون: |
Jiang, Song1 (AUTHOR) jiang@iapcm.ac.cn, Zhou, Chunhui2 (AUTHOR) zhouchunhui@seu.edu.cn |
| المصدر: |
Journal of Differential Equations. Mar2025, Vol. 420, p52-98. 47p. |
| مصطلحات موضوعية: |
*COUETTE flow, *NAVIER-Stokes equations, *BOUNDARY layer (Aerodynamics), *SHEAR flow, *VISCOSITY solutions, *EULER equations |
| مستخلص: |
We study the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow in the absence of any external force in two-dimensional domain Ω = (0 , L) × (0 , 2). Under the assumption 0 < L ≪ 1 , we prove that there exist smooth solutions to the steady Navier-Stokes equations which are stable under infinitesimal perturbations of plane Poiseuille-Couette flow. In particular, if the basic flow is the Couette flow, then through a formal asymptotic expansion including the Euler correctors and weak boundary layer correctors with different scales near the rigid walls y = 0 and y = 2 , we can prove that for any finite disturbance o (1) of the Couette flow in horizontal direction, there still exist stable smooth solutions to the steady Navier-Stokes equations. Finally, based on the same linear estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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