Related papers: Weak-strong uniqueness of dissipative measure-valu…
We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality approach. This construction is well suited to apply the…
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
As a framework for handling low Mach number limits we consider a notion of measure-valued solution of the incompressible Euler system which explicitly formulates the usually suppressed dependence on the pressure variable. We clarify in…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
We propose and analyze a new asymptotic preserving (AP) finite volume scheme for the multidimensional compressible barotropic Euler equations to simulate low Mach number flows. The proposed scheme uses a stabilized upwind numerical flux,…
Matrix measures induced by vector norms are widely used in contraction theory of nonlinear dynamical systems. A natural and important robustness question is whether negativity of a matrix measure is preserved under arbitrary nonnegative…
We study the connection between mild and weak solutions for a class of measure-valued evolution equations on the bounded domain $[0,1]$. Mass moves, driven by a velocity field that is either a function of the spatial variable only,…
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
There exist methods for determining effective conservative interactions in coarse grained particle based mesoscopic simulations. The resulting models can be used to capture thermal equilibrium behavior, but in the model system we study do…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space $\R^3$ when the positive charged ion flow provides a spatially uniform…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
We propose a framework for unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
The study of metamaterials and architected materials has intensified interest in continuum mechanics models that capture size-dependent microstructure interactions. Among these, Consistent Couple-Stress Theory (C-CST) incorporates…
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…