Seminar on partial differential equations

Problems of linearized Navier-Stokes equations in frequency domain

For aeroacoustics applications, it is very tempting to work with linearized equations in frequency domain. Not only are the solutions simpler in overall, but also some variables are defined solely in the frequency domain (such as impedance and related quantities). In quiescent media, the frequency domain calculations enjoy well-deserved popularity. However, great caution must be taken when applying the same mathematical steps to linearized Navier-Stokes equations, although technically there is no apparent difficulty. The talk will present a specific case of the method failure: despite the fact that the acoustic quantities are indeed small, the hydrodynamics cannot be governed by the linearized equations. The final part of the talk will be a discussion of some papers that use the linearized equations.