Related papers: Relative entropy inequality for capillary fluids w…
We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab,…
We prove weak-strong uniqueness in the class of admissible measure-valued solutions for the isentropic Euler equations in any space dimension and for the Savage-Hutter model of granular flows in one and two space dimensions. For the latter…
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We…
A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…
We study two problems related to flow equivalence of shift spaces. The first problem, the classification of $S$-gap shifts up to flow equivalence, is partially solved with the establishment of a new invariant for the sofic $S$-gap shifts…
A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant $\gamma\in [1,3)$. This formulation allows a family of invariant regions in the phase plane for…
Using viscous relativistic hydrodynamics we show that systematic studies of the impact parameter dependence of the eccentricity scaled elliptic flow can distinguish between different models for the calculation of the initial source…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
We study a hydrodynamic limit of a system of coupled kinetic and fluid equations under a strong local alignment force and a strong Brownian motion. More precisely, we consider the Vlasov-Fokker-Planck type equation and compressible…
We prove a rigorous convergence result for the compressible to incompressible limit of weak entropy solutions to the isothermal 1D Euler equations.
We examine the applicability of various model profiles for the liquid/vapor interface by X-ray reflectivities on water and ethanol and their mixtures at room temperature. Analysis of the X-ray reflecivities using various density profiles…
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…
We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
We consider the Cauchy problem for a strictly hyperbolic, $n\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation. We show that the solutions of the viscous approximations…
Flows with deformable interfaces are commonly controlled by applying an external field or modifying the boundaries that interact with the fluid, but realizing such solutions can be demanding or impractical in various scenarios. Here, we…