Final Report Summary - ULD3DNSE (Uniqueness of solutions of the three-dimensional Navier-Stokes equations for large sets of data)
Our aim has been to understand further the solutions of the three-dimensional incompressible Navier–Stokes equations (3DNSE).
Whether or not these equations possess smooth solutions that exist for all time for any smooth initial condition is one of the Clay Foundation’s Million Dollar Millennium Prize Problems. Most of our work during the project period has been based on work of Fursikov from the 1970s, treating not the Navier–Stokes equations themselves but the equations for the evolution of the moments of an initial measure.
The remarkable thing about this approach is that while the Navier–Stokes equations themselves are nonlinear, the moment equations are linear.
Whether or not these equations possess smooth solutions that exist for all time for any smooth initial condition is one of the Clay Foundation’s Million Dollar Millennium Prize Problems. Most of our work during the project period has been based on work of Fursikov from the 1970s, treating not the Navier–Stokes equations themselves but the equations for the evolution of the moments of an initial measure.
The remarkable thing about this approach is that while the Navier–Stokes equations themselves are nonlinear, the moment equations are linear.
