Related papers: Weak solutions to gamma-driven stochastic differen…
We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority…
We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians…
We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of a constant. We show that in the diffusive time-scale, in all dimensions, the density defect evolves as the solution of a viscous…
Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However,…
This paper is concerned with the existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation on real line. By introducing some new variables, the equation is transformed into two different semi-linear systems.…
We study the vortex dynamics in an evolutive flow. We carry out the statistical analysis of the resulting time series by means of the joint use of a compression and an entropy diffusion method. This approach to complexity makes it possible…
In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the…
We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solutions are considered and compared. We establish existence and regularity results. In particular…
We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…
We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of…
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a…
The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples the diffusive interface model with…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
In this article, we study the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation. This model contains the terms $\cal{D}_t^\alpha(u_t)$ and $\cal{D}_t^\alpha u $ (with $\alpha \in(0,1)$), where…
We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an…
We consider weak solutions of the spatially inhomogeneous Landau equation with hard potentials ($\gamma \in (0,1]$), under the assumption that mass, energy, and entropy densities are under control. In this regime, with arbitrary initial…