相关论文: Nonlinear Vlasov-Fokker-Planck equations: From gen…

We introduce a continuous Galerkin finite element discretization of the non-hydrostatic Boussinesq approximation of the Navier-Stokes equations, suitable for various applications such as coastal ocean dynamics and ice-ocean interactions,…

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the…

The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…

The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion…

We establish an exact equivalence between the Functional Renormalization Group (FRG) and the Ricci flow modified by a potential-driven diffeomorphism. By reformulating the Polchinski exact renormalization group equation into an…

We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…

Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled…

We discuss a general class of nonlinear mean-field Fokker-Planck equations [P.H. Chavanis, Phys. Rev. E, 68, 036108 (2003)] and show their applications in different domains of physics, astrophysics and biology. These equations are…

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…

We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle…

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with an arbitrary potential…

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…

The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…

A new magnetization equation recently derived from irreversible thermodynamics is employed to the calculation of an increase of ferrofluid viscosity in a magnetic field. Results of the calculations are compared with those obtained on the…

This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…

We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…

In this work, we first derive the evolution equation for the general energy-momentum moment of $\delta f$, where $\delta f$ is the deviation from the local equilibrium phase space density. We then introduce a relativistic extension of…

This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov-Fokker-Planck equation in which the Laplacian is replaced by a fractional Laplacian. The evolution of the density is governed by a fractional heat…

In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…