Stability of Inflow Problem for Hyperbolic Systems

Abstract

Inflow BC plays a critical role in the study of hyperbolic PDE in a bounded domain. We establish $W^{1,\infty }$ stability for 1D hyperbolic conservation laws with inflow data in a bounded interval, and $W^{2,3+}$ stability of a large class of shear flows for the 3D incompressible Euler system with inflow BC in finite square or circular pipes.

arXiv commentWe add an appendix for 3D Euler with velocity inflow BC