The APDE seminar on Monday, 9/30, will be given by Koji Ohkitani (RIMS, Kyoto University) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto () or Mengxuan Yang ().
Title: Numerical determination of the self-similar profile
for the 3D Navier-Stokes equations and its applications
Abstract: We present the forward self-similar profile for the 3D Navier-Stokes
equations, representing the late stage of decaying Navier-Stokes flows.
The existence of such a profile has been known, but its precise functional
form has not been determined numerically, let alone mathematically.
Here we determine the profile for the first time using numerical methods.
This has been achieved by a combination of two things; a numerical method
of solving the Navier-Stokes equations in the whole space and the explicit
form of the linearised solution. Taking the initial data from the
linearised solution, we solve the fully-nonlinear Navier-Stokes equations
to observe its convergence to a steady solution in the dynamically scaled
space. We have confirmed that the nonlinear correction is small,
consistent with the previous perturbative analysis. Applications of the
self-similar profile are briefly discussed.