Related papers: Sharp a-contraction estimates for small extremal s…
The aim of this work is to prove the weak-strong uniqueness principle for the compressible Navier-Stokes-Poisson system on an exterior domain, with an isentropic pressure of the type $p(\varrho)=a\varrho^{\gamma}$ and allowing the density…
In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of…
We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution toward the unique entropy solution…
We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the…
We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order Rusanov-Burstein-Mirin (RBM), and the fifth-order alternative…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: \pt \rho +\px \Psi(\rho, u)=0 \pt u+\px…
This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and…
We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches,…
We extend results on robust exponential mixing for geometric Lorenz attractors, with a dense orbit and a unique singularity, to singular-hyperbolic attracting sets with any number of (either Lorenz- or non-Lorenz-like) singularities and…
In shockwave theory, the density, velocity and pressure jumps are derived from the conservation equations. Here, we address the physics of a weak shock the other way around. We first show that the density profile of a weak shockwave in a…
Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$…
We prove the nonlinear stability of the planar viscous shock up to a time-dependent shift for the three-dimensional (3D) compressible Navier-Stokes equations under the generic perturbations, in particular, without zero mass conditions.…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
This paper is concerned with entropy solutions of scalar conservation laws of the form $\partial_{t}u+\diver f=0$ in $\mathbb{R}^d\times(0,\infty)$. The flux $f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension of…
We study the following class of scalar hyperbolic conservation laws with discontinuous fluxes: \partial_t\rho+\partial_xF(x,\rho)=0. The main feature of such a conservation law is the discontinuity of the flux function in the space variable…
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…