The analysis shows no global smooth solutions for the Navier-Stokes equation, indicating limitations in laminar flow behavior and impact at high Reynolds numbers.
Key Points
The study proves the non-existence of global smooth solutions for the Navier-Stokes equation under specific conditions.
At high Reynolds numbers, disturbances in flow can amplify, leading to unbounded velocity gradients.
The method involves decomposing unsteady laminar flow into time-averaged and disturbance components.
Results underscore challenges in predicting smooth solution behavior for fluids described by the Navier-Stokes equation.