Existence of Large Boundary Layer Solutions to Inflow Problem of 1D Full Compressible Navier-Stokes Equations

2025/04/30 by Yi Wang, Wang, Yi, Yong‐Fu Yang +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2504.21830

openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Time-Asymptotic Stability of Generic Riemann Solutions for Compressible Navier–Stokes–Fourier Equations
• Time-asymptotic stability of generic Riemann solutions for compressible Navier-Stokes-Fourier equations
• Large-time behavior of composite waves of viscous shocks for the barotropic Navier-Stokes equations
• Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
• Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations
• L²-contraction for shock waves of scalar viscous conservation laws
• Stationary waves to viscous heat-conductive gases in half space: existence, stability and convergence rate
• Stability of Wave Patterns to the Inflow Problem of Full Compressible Navier-Stokes Equations
• Nonlinear asymptotic stability of viscous shock profiles for conservation laws

Cited by

• Asymptotic behavior toward viscous shocks for the outflow problem of barotropic Navier-Stokes equations

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