[HG_AP] Stability of the one-dimensional compressible Euler system with boundary
ABSTRACT
The stability theory of entropy solutions to the compressible Euler system on a half-line with prescribed boundary conditions, such as inflow, outflow, and impermeable boundary conditions, remains largely open. It is worth emphasizing that establishing the stability of even a single reflected shock at the boundary has been a highly challenging problem. In this talk, I will briefly review the classical stability theory for small-BV entropy solutions in the whole-space setting and then turn to the half-line problem, where I will present recent progress on the stability of entropy solutions in the presence of a boundary. This talk is based on joint work with Moon-Jin Kang (KAIST), Jiayun Meng (The University of Texas at Austin), and Alexis Vasseur (The University of Texas at Austin).
