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# fluid dynamics

## Latest Articles

### Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

### Mathematicians Coax Fluid Equations Into Nonphysical Solutions

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

### Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

### An Injection of Chaos Solves Decades-Old Fluid Mystery

In the 1960s, drillers noticed that certain fluids would firm up if they flowed too fast. Researchers have finally explained why.

### Mathematicians Prove Melting Ice Stays Smooth

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

### Mathematicians Identify Threshold at Which Shapes Give Way

A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

### New Quantum Algorithms Finally Crack Nonlinear Equations

Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.

### A Mathematician’s Unanticipated Journey Through the Physical World

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

### An Unexpected Twist Lights Up the Secrets of Turbulence

Having solved a central mystery about the “twirliness” of tornadoes and other types of vortices, William Irvine has set his sights on turbulence, the white whale of classical physics.