How Did Mathematicians Finally Solve the 140-Year-Old Boltzmann Equation?

[fourier jr]

I've never heard of this before. Maybe I should learn more physics:

Using modern mathematical techniques from the fields of partial differential equations and harmonic analysis — many of which were developed during the last five to 50 years, and thus relatively new to mathematics — the Penn mathematicians proved the global existence of classical solutions and rapid time decay to equilibrium for the Boltzmann equation with long-range interactions. Global existence and rapid decay imply that the equation correctly predicts that the solutions will continue to fit the system’s behavior and not undergo any mathematical catastrophes such as a breakdown of the equation’s integrity caused by a minor change within the equation. Rapid decay to equilibrium means that the effect of an initial small disturbance in the gas is short-lived and quickly becomes unnoticeable.

http://www.upenn.edu/pennnews/news/university-pennsylvania-mathematicians-solve-140-year-old-boltzmann-equation-gaseous-behaviors

http://www.pnas.org/content/107/13/5744.abstract?sid=08ced618-f372-4c0d-a80c-64786d92c3ff

 

[ABarrios]

Thats great!

 

[sEsposito]

Quite a remarkable achievement. Just another example of how PDEs have changed mathematics.