Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas
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 ℝn (n ≥ 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∈ (0,1), the approximation error is of order O(μα).
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BibTeX
@misc{hashimoto2026inviscid,
title = {{Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas}},
author = {Itsuko Hashimoto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29074},
eprint = {2610.29074},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29074},
}
RIS
TY - UNPB
TI - Inviscid Limit Problem for Radially Symmetric Stationary States of Viscous and Heat-Conductive Ideal Gas
AU - Itsuko Hashimoto
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29074
UR - https://arxiv.org/abs/2610.29074
AB - 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 ℝ^n (n ≥ 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∈ (0,1), the approximation error is of order O(μ^α).
ER -