Infinite energy solutions to inelastic homogeneous Boltzmann equations

Infinite Energy Solutions to the Homogeneous Boltzmann Equation

The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are ...

On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations

Infinite Energy Solutions for Dissipative Euler Equations in R 2

We study the system of Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the further development of the weighted energy theory for the Navier–Stokes and Euler type problems. In addition, the existence of weak locally compact ...

Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tail...

Moment Inequalities and High-energy Tails for the Boltzmann Equations with Inelastic Interactions

We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−r|v|s) for |v| large. The values of s, which we call the orders of tail...