Thomas Eiter (University Kassel): Far-field behavior of oscillatory viscous flow past an obstacle

Zoom Link: https://uni-kassel.zoom.us/j/96217091997?pwd=RVRaVVBRclFJYU9jczNZSWF3SXI2QT09

Meeting ID: 962 1709 1997
Passcode: cauchy

Abstract:

We consider the time-periodic flow of an incompressible viscous fluid past an obstacle moving with constant non-zero velocity. Using the time-periodic fundamental solution to the associated linearized problem in the whole space, we first derive new representation formulas for weak solutions under suitable regularity assumptions. These formulas lead to asymptotic expansions of the velocity and the pressure field at spatial infinity, which imply sharp pointwise decay estimates and reveal new terms that, in comparison with the situation of a steady flow, cause a slower decay rate in case of general time-periodic boundary flux. Finally, we use the decay estimates in order to study an approximation of the flow by problems on truncated domains.