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arXiv · 2610.07574

Weak-BV Stability and Inviscid Limits for Barotropic Flows with Outflow Boundary Conditions

Jiayun Meng·Alexis F. Vasseur
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Abstract

Boundary value problems for systems of conservation laws, including inviscid compressible flows, arise naturally in physical models such as shallow water flow in a canal, where fluid may leave the domain through the boundary. In contrast to the Cauchy problem, the inviscid limit is highly sensitive to the underlying viscous model: different viscous regularizations may select different effective boundary conditions for the limiting system. In this paper, we show that small BV solutions of the one-dimensional compressible barotropic Euler equations arise as inviscid limits of the barotropic Navier-Stokes system for the outflow boundary problem. We work with the physically meaningful effective boundary condition selected by the Navier-Stokes system for the limiting Euler solutions. Moreover, going beyond smooth flows or a fixed class of Riemann solutions, our stability results apply to small BV solutions exhibiting general wave patterns and complicated configurations generated by interactions with the outflow boundary, including reflected shocks.

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Jiayun Meng, Alexis F. Vasseur. 2026-10-06. Weak-BV Stability and Inviscid Limits for Barotropic Flows with Outflow Boundary Conditions. https://arxiv.org/abs/2610.07574

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