Homoenergetic Solutions for the Boltzmann Equation

Explore homoenergetic solutions of the Boltzmann equation in this lecture from the Hausdorff Junior Trimester Program on Kinetic Theory. Delve into the dynamics of Boltzmann gases under shear, expansion, or compression in nonequilibrium situations. Compare the well-posedness theory of homoenergetic solutions with that of homogeneous solutions, and examine their distinct long-time asymptotics. Investigate cases where the asymptotic behavior deviates from Maxwellian distributions, leading to particle distributions that do not satisfy the detailed balance condition. Learn about various possible long-time asymptotics of homoenergetic solutions and discuss open problems in this field. The lecture presents joint work with R.D. James and J.J.L. Velázquez, offering insights into this specialized area of kinetic theory.