Abstract: This paper proves the existence of small-amplitude global-in-time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation without angular ...

Mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases.

Kinetic equations serve as fundamental tools for understanding the statistical behaviour of particles within a system, bridging the microscopic world of individual particle interactions with ...

It has taken 140 years, but only now do we have mathematical proof that a seminal equation describing the behaviour of gases is correct. Robert Strain and Philip Gressman at the University of ...

We solve the nonlinear Poisson–Boltzmann (P–B) equation of statistical thermodynamics for the external electrostatic potential of a uniformly charged flat plate immersed in an unbounded strong aqueous ...

Science popularization has its legends and heroes, just like any other field, though I’ve heard no plans as yet to open a Hall of Fame. Should that day come, one of the first inductees would ...

This paper studies the transition occurring in the type of singularity, induced by a line charge to solutions of the Poisson-Boltzmann equations in R2, at some critical value of the linear charge ...

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer. In 1900, the great mathematician David Hilbert presented a list of 23 unsolved ...