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1. Differential Equations

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   Fluid Dynamics (Navier-Stokes Equations)
   The Navier-Stokes equations describe the motion of viscous fluid substances. They are notoriously complex, being non-linear, second-order PDEs. The difficulty in finding general analytical solutions has led to the Clay Mathematics Institute offering a million-dollar prize for proving whether smooth solutions exist for all time in three dimensions. The inclusion of the viscous term, which model…