Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas

Itsuko Hashimoto

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arXiv · 2610.29074

Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas

Itsuko Hashimoto

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Abstract

We study the zero-viscosity limit of radially symmetric stationary solutions for the inflow and outflow problems for a viscous and heat-conductive polytropic ideal gas in the exterior of a ball in $\mathbb{R}^n$ ($n \geq 3$), under prescribed boundary and far-field conditions. The far-field velocity is assumed to be zero, and the solutions are considered in a sufficiently small neighborhood of the far-field state. In the zero-viscosity limit, the viscous terms disappear from the momentum equation, while the heat-conduction term remains in the energy equation. For the outflow problem, we prove that the viscous stationary solution converges uniformly to the corresponding stationary solution of the heat-conductive inviscid system, with convergence rate $O(μ)$. For the inflow problem, a boundary layer appears near the inner boundary. We show that the viscous stationary solution is uniformly approximated by the superposition of the limiting stationary solution and a boundary-layer profile. Here, the boundary layer appears only for the density and velocity, whereas no boundary-layer appears for the temperature. Moreover, for any $α\in (0,1)$, the approximation error is of order $O(μ^α)$.

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Itsuko Hashimoto. 2026-10-21. Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas. https://arxiv.org/abs/2610.29074

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