相关论文: A geometric approximation to the Euler equations: …
The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient,…
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…
We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles…
The general pressure equation (GPE) is a new method proposed recently by Toutant (J. Comput. Phys., 374:822-842 (2018)) for incompressible flow simulation. It circumvents the Poisson equation for the pressure and performs better than the…
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport…
We consider the compressible Euler equations with potential temperature transport, a system widely used in atmospheric modelling to describe adiabatic, inviscid flows. In the low Mach number regime, the equations become stiff and pose…
We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure valued solutions of the incompressible Euler equations. The resulting approximate young measures are proved to…
In this paper, we study flexibility of weak solutions to the Monge-Amp\`ere system (MA) via convex integration. This new system of Pdes is an extension of the Monge-Amp\`ere equation in $d=2$ dimensions, naturally arising from the…
In this paper we investigate the hydrodynamic limit of the Boltzmann-Monge-Ampere system in the so-called quasineutral regime. We prove the convergence of the Boltzmann-Monge-Ampere system to the Euler equation by using the relative entropy…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
A system of linear homogeneous algebraic equations for coupling constant ratios of vector-mesons to hadrons is derived by imposing an asymptotic behaviuor upon the VMD pole parametrization of an hadron electromagnetic form factor. A similar…
In this article, we develop the $C^1$-nonconforming $C^0$-conforming virtual element method (VEM) for the vanishing moment approximation of the second-order fully nonlinear Monge-Amp\`ere equation in two dimensions. In the vanishing moment…
In this work, we study the orbital stability of steady states and the existence of blow-up self-similar solutions to the so-called Vlasov-Manev (VM) system. This system is a kinetic model which has a similar Vlasov structure as the…
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge…
Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elements in a way unaffected by any pressure or…
Motivated by the fundamental model of a collisionless plasma, the Vlasov-Maxwell (VM) system, we consider a related, nonlinear system of partial differential equations in one space and one momentum dimension. As little is known regarding…
We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly…
Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…
We study in this paper the non-relativistic limit from Vlasov-Maxwell to Vlasov-Poisson, which corresponds to the regime where the speed of light is large compared to the typical velocities of particles. In contrast with…