Related papers: Stochastic conservation laws: weak-in-time formula…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to…
We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an…
We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…
The notion of Kruzhkov entropy solution was extended by the first author in 2007 to conservation laws with a fractional laplacian diffusion term; this notion led to well-posedness for the Cauchy problem in the $L^\infty$-framework. In the…
We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume…
In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes…
We study nonlinear hyperbolic conservation laws posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable), a class of…
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…
Chang's lemma is a useful tool in additive combinatorics and the analysis of Boolean functions. Here we give an elementary proof using entropy. The constant we obtain is tight, and we give a slight improvement in the case where the…
The formulation of quantum mechanics within the framework of entropic dynamics includes several new elements. In this paper we concentrate on one of them: the implications for the theory of time. Entropic time is introduced as a…
In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by…
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…
We describe in great generality features concerning constrained entropic, functional variational problems that allow for a broad range of applications. Our discussion encompasses not only entropies but, potentially, any functional of the…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
We deal with the 3D inviscid Leray-{\alpha} model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves…