Related papers: Computing oscillatory solutions of the Euler syste…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
In this paper, we are concerned with the hydrodynamic limit to rarefaction waves of the compressible Euler system for the Landau equation with Coulomb potentials as the Knudsen number $\epsilon>0$ is vanishing. Precisely, whenever…
We study convergence of a mixed finite element finite volume numerical scheme for the isentropic Navier-Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that…
This paper deals with the derivation and analysis of a compressible Euler-type equation with singular commutator, which is derived from a hyperbolic limit of the kinetic description to the Cucker-Smale model of interacting individuals
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Consider the scaling $\varepsilon^{1/2}(x-Vt)\to x,\ \varepsilon^{3/2}t\to t$ in the Euler-Poisson system for ion-acoustic waves \eqref{equ1}. We establish that as $\varepsilon\to 0$, the solutions to such Euler-Poisson system converge…
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure…
Let $K\subset\mathbb{C}$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$-regular sequences of polynomials, that center on $K$ and under the sequences of…
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…
We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise…
We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our…
On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation for k=n. We…
We proved the convergence of a sequence of 2 dimensional comapct Kahler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifods to a…
We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher…
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear…
Using the generalized Young measure theory, we extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce the concept of generalized Young measure solutions. We prove the…
We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2, \ \ \delta>0$. In the framework of dissipative measure-valued solutions, we show…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
We provide representations of Euler's constant $\gamma=0.577...$ as series which converge geometrically fast (but use coefficients whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are discussed.