PDEA Seminar: The asymptotic far field of time-periodic flow past an obstacle

Abstract: We consider the time-periodic flow of an incompressible viscous fluid past an obstacle moving with constant non-zero velocity. We derive new representation formulas for weak solutions under suitable regularity assumptions, which are based on time-periodic fundamental solutions to a corresponding linearization. These formulas lead to far-field expansions of the velocity and the pressure, which imply sharp pointwise decay estimates. In comparison with the situation of a time-periodic flow in the whole space or of a time-independent flow, these asymptotic expansions contain novel terms that reveal new effects, which may cause a slower decay rate. The resulting decay properties can further be used

to study the approximation of the original exterior-domain problem by bounded-domain problems with suitable boundary conditions.

This is a seminar in the PDEs and Applications seminar series