Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study many models, which can explain pattern formation. The modulations patterns, occurring on long and temporal scales, cannot be captured linear approximation analysis. Here, we show that, starting from general model wit...

In this document we discuss the long time behaviour for homogeneous Landau-Fermi-Dirac equation in hard potential case. Uniform estimates statistical moments and Sobolev regularity are presented used to prove exponential relaxation of non degenerate distributions Fermi-Dirac statistics. All these results valid rather general initial datum. An important feature is independence with respect quant...

Abstract. We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft ...

We investigate the infrared behaviour of gluon and ghost propagators in Landau gauge QCD by means of an exact renormalisation group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimisation procedure is devised to remove residual regulator dependences. In Landau gauge QCD this framework is used to determine th...