带外流边界条件的正压流的弱BV稳定性与无粘极限
Weak-BV Stability and Inviscid Limits for Barotropic Flows with Outflow Boundary Conditions
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- The University of Texas at Austin（德克萨斯大学奥斯汀分校）
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中文总结 AI 辅助
本文证明一维可压缩正压欧拉方程的小BV解可作为外流边界问题的正压纳维-斯托克斯系统的无粘极限，并采用物理有效的边界条件，稳定性结果涵盖一般波模式与反射激波等复杂结构。
中文摘要 AI 辅助
守恒律系统（包括无粘可压缩流）的边值问题自然出现在物理模型中，例如运河中的浅水流动，其中流体可能通过边界离开区域。与柯西问题相比，无粘极限对底层粘性模型高度敏感：不同的粘性正则化可能为极限系统选择不同的有效边界条件。在本文中，我们证明一维可压缩正压欧拉方程的小BV解可作为外流边界问题的正压纳维-斯托克斯系统的无粘极限而出现。我们采用由纳维-斯托克斯系统为极限欧拉解选择的具有物理意义的有效边界条件。此外，超越光滑流或固定类别的黎曼解，我们的稳定性结果适用于具有一般波模式和由与外流边界相互作用（包括反射激波）产生的复杂结构的小BV解。
英文摘要
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.
