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arXiv · 2608.21738

Existence of Large Boundary Layer Solutions for the Outflow Problem of Full Compressible Navier-Stokes Equations

Tianle Wang·Yi Wang·Qiuyang Yu
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Abstract

We investigate the existence and non-existence of large-amplitude boundary layer solutions to the outflow problem for the one-dimensional full compressible Navier-Stokes equations on the half-line $\mathbb{R}_+$. Through a delicate global phase-plane analysis, we substantially extend the small-amplitude boundary layer solutions obtained via the center-manifold approach to the large-amplitude regime. Based on the sign of $M_+-1$ (with $M_+$ denoting the Mach number at the right end state) and the Prandtl-number-related parameter $\zeta$, we provide a complete characterization of the existence and non-existence of large-amplitude boundary layer solutions for this half-space outflow problem. In sharp contrast to the corresponding inflow problem, boundary layer solutions to the outflow problem are permitted to be non-monotone, and their existence region in the phase plane can be an open set.

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Tianle Wang, Yi Wang, Qiuyang Yu. 2026-08-22. Existence of Large Boundary Layer Solutions for the Outflow Problem of Full Compressible Navier-Stokes Equations. https://arxiv.org/abs/2608.21738

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