For nearly two centuries, all kinds of researchers interested in how fluids flow have turned to the Navier-Stokes equations. But mathematicians still harbor basic questions about them. Foremost among them: How well do the equations adhere to reality?
A new paper set to appear in the Annals of Mathematics has chipped away at that question, proving that a once-promising class of solutions can contain physics-defying contradictions. The advance is another step toward understanding the discrepancy between Navier-Stokes and the physical world — a mystery that underlies one of math’s most famous open problems.
“It’s very impressive,” said Isabelle Gallagher, a mathematician at the École Normale Supérieure in Paris and Université Paris Cité. “I mean, it’s the first time you really have [these] solutions which are not unique.”
