Navier-Stokes Existence and Smoothness

Unsolved Problem

It has not yet been proven that the Navier-Stokes equations:

always exist in ordinary $3$-dimensional space

if they do exist, they do not contain any singular points.

Progress

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Source of Name

This entry was named for Claude-Louis Navier and George Gabriel Stokes.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Millennium Prize problems
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Navier-Stokes equation
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Millennium Prize problems
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $18$: Millennium Prize problems: $5$.
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $23$: Millennium Prize problems: $5$.