发表机构
Korea Advanced Institute of Science and Technology; The University of Texas at Austin（韩国科学技术院; 德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一维等熵欧拉系统在流入和流出边界条件下小BV解的适定性，建立了首个弱BV稳定性与唯一性理论，关键方法为验证边界集与a-压缩框架相容。
AI 中文摘要
我们研究了半直线上带流入和流出边界条件的一维等熵欧拉系统的小BV解的适定性。这些边界条件由Navier-Stokes边界层和零速激波确定的可容许迹集来表述。对于流入和流出问题，我们构造了取值于亚音速区域的小BV解。这些解是唯一的，并满足定量稳定性估计\begin{align*} \\|U(\cdot, t)-V(\cdot, t)\\|_{L^2} \lesssim \sqrt{\\|U(\cdot, 0) - V(\cdot, 0)\\|_{L^2}} \\,, \end{align*}该估计对任何此类小BV解$V$和任何满足强迹性质及流入/流出边界条件的$L^\infty$熵解$U$均成立。特别地，我们强调$U$可以取亚音速区域之外的值，且不必具有有界变差或由前向追踪格式构造。这建立了流入和流出初边值问题的首个弱BV稳定性和唯一性理论。一个关键困难在于验证边界集与$a$-压缩框架相容，以及证明前向追踪极限满足规定的流入/流出条件。
英文摘要
We study the well-posedness of small BV solutions to the one-dimensional isentropic Euler system on the half-line under inflow and outflow boundary conditions. These boundary conditions are formulated in terms of admissible trace sets determined by Navier--Stokes boundary layers and zero-speed shocks. For both the inflow and outflow problems, we construct small BV solutions taking values in the subsonic region. These solutions are unique and satisfy the quantitative stability estimate \begin{align*} \|U(\cdot, t)-V(\cdot, t)\|_{L^2} \lesssim \sqrt{\|U(\cdot, 0) - V(\cdot, 0)\|_{L^2}} \, , \end{align*} which holds for any such small BV solution $V$ and any $L^\infty$ entropy solution $U$ satisfying the strong trace property and the inflow/outflow boundary conditions. In particular, we emphasize that $U$ may take values outside the subsonic region and need not have bounded variation or be constructed by the front tracking scheme. This establishes the first weak-BV stability and uniqueness theory for inflow and outflow initial-boundary value problems. A key difficulty lies in verifying that the boundary set is compatible with the $a$-contraction framework, and in proving that the front-tracking limit satisfies the prescribed inflow/outflow conditions.
