Stability of Inflow Problem for Hyperbolic Systems

TL;DR

This paper proves stability results for hyperbolic PDEs with inflow boundary conditions, including 1D conservation laws and 3D shear flows in pipes, advancing understanding of inflow boundary effects.

Contribution

It establishes new stability estimates in Sobolev spaces for hyperbolic systems with inflow boundary conditions, covering both 1D and 3D cases.

Findings

W^{1,∞} stability for 1D hyperbolic conservation laws with inflow data

W^{2,3+} stability for shear flows in 3D incompressible Euler system

Stability results applicable to bounded domains with inflow boundaries

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.