Abstract: In this talk, I will discuss how a smooth unknown background flow can be recovered from the local source-to-solution map for the compressible Euler's equations. We start with the standard microlocal analysis and higher order linearization method for nonlinear hyperbolic inverse problems, and demonstrate how non-zero vorticity helps pin down the exact solution of the background flow. The talk is based on joint work with Gunther Uhlmann and Jian Zhai.