Steady compressible Navier-Stokes-Fourier system with slip boundary conditions arising from kinetic theory

2024/09/18 by Renjun Duan, Duan, Renjun, Junhao Zhang +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2409.11809

openalex publication_date 2024/09/18 · openalex created_date 2024/10/25 · openalex updated_date 2026/07/28

Abstract

This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain (0,1)×\mathbbT² with a class of generalized slip boundary conditions that were systematically derived from the Boltzmann equation by Coron \citeCoron-JSP-1989 and later by Aoki et al \citeAoki-Baranger-Hattori-Kosuge-Martalo-Mathiaud-Mieussens-JSP-2017. We establish the existence and uniqueness of strong solutions in (L₀²∩ H²(Ω))× V³(Ω)× H³(Ω) provided that the wall temperature is near a positive constant. The proof relies on the construction of a new variational formulation for the corresponding linearized problem and employs a fixed point argument. The main difficulty arises from the interplay of velocity and temperature derivatives together with the effect of density dependence on the boundary.

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