This memoir studies the stability of symmetric fluid flows in a two-dimensional channel, including the classical Poiseuille flow. Building on formal predictions from the 1940s, instability in a specific parameter regime was rigorously established about a decade ago. This work completes the picture by proving that outside that parameter region, these flows are stable. The analysis centers on the Orr–Sommerfeld operator, a key mathematical tool for tracking how small disturbances evolve in fluid motion. The authors precisely identify when the operator remains bounded, offering a sharp characterization of the flow's stability boundaries.