Related papers: Schauder estimates for stochastic transport-diffus…
We construct a slowly varying space-time dependent holographic superfluid and compute its transport coefficients. Our solution is presented as a series expansion in inverse powers of the charge of the order parameter. We find that the shear…
Transport coefficients are of crucial importance in theoretical as well as experimental studies. Despite substantial research on classical hard sphere/disk gases in low and high density regimes, a thorough investigation of transport…
In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with…
We present a physical example, where a fractional (both in space and time) Schr\"odinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the…
We show how to compute transport coefficients in gauge theories by considering the expansion of the Kubo formulas in terms of ladder diagrams in the imaginary time formalism. All summations over Matsubara frequencies are performed and the…
We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on IR^d for d greater or equal to 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial…
We generalize a well-known result of L. Caffarelli on Lipschitz estimates for optimal transportation $T$ between uniformly log-concave probability measures. Let $T : \R^d \to \R^d$ be an optimal transportation pushing forward $\mu =…
Modeling QCD at large temperature with a simple holographic five dimensional theory encoding minimal breaking of conformality, allows for the calculation of all the transport coefficients, up to second order, in terms of a single parameter.…
This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated…
We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump L\'evy transport noise satisfies a dissipative deterministic equation involving a fractional Laplace-type operator. To this…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
We investigate the optimal H\"older continuity and hitting probabilities for systems of stochastic heat equations and stochastic wave equations driven by an additive fractional Brownian sheet with temporal index $1/2$ and spatial index…
We study a quite general class of stochastic dispersive equations with linear multiplicative noise, including especially the Schr\"odinger and Airy equations. The pathwise Strichartz and local smoothing estimates are derived here in both…
We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients.…
We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schr\"{o}dinger equation with nonlinear multiplicative jump noise in the Marcus…
We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with H\"older noise and potential whose range is large in comparison with the typical distance between…
We consider a diffusion process under a local weak H\"{o}rmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains…
This paper is concerned with the global smooth non-vacuum solutions with large data to the Cauchy problem of the one-dimensional compressible Navier-Stokes equations with degenerate temperature dependent transport coefficients which satisfy…
We study the optimal control of an infinite-dimensional stochastic system governed by an SDE in a separable Hilbert space driven by cylindrical stable noise. We establish the existence and uniqueness of a mild solution to the associated HJB…
In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degenerate nonlocal equation in $\mathbb R^{2d}$ with H\"older…