CORDIS Project
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This project investigates the uniqueness of solutions to the three-dimensional Navier-Stokes equations, a key model for fluid dynamics. It aims to establish conditions under which unique solutions exist for large data sets, providing a theoretical framework for verifying these solutions numerically and enhancing our un…
The three-dimensional Navier-Stokes equations are the fundamental mathematical model of fluid flow.
However, currently we only know that unique solutions exist for all time for 'small' data (initial condition and forcing); for 'large' data they can only be guaranteed to exist for a short time.
The existence of unique smooth solutions that exist for all time for any choice of data is one of the Clay Foundation's Million Dollar Millennium Prize Problems, and is exceedingly hard.
The goal of this p…
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