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We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric…

Analysis of PDEs · Mathematics 2015-06-11 Gui-Qiang G. Chen , Mikhail Perepelitsa

To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number.…

Fluid Dynamics · Physics 2018-03-08 Yudong Zhang , Aiguo Xu , Guangcai Zhang , Zhihua Chen , Pei Wang

We are concerned with the isothermal limit of entropy solutions in $L^\infty$, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in $L^\infty$ of the isentropic Euler…

Analysis of PDEs · Mathematics 2023-02-07 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang

In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations.…

Numerical Analysis · Mathematics 2013-07-10 Giacomo Dimarco

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…

Analysis of PDEs · Mathematics 2021-04-27 Sébastien Boyaval , Mark Dostalík

By refining the method proposed in arXiv:2010.07660, entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Noether conserved charge in the Einstein gravity…

General Relativity and Quantum Cosmology · Physics 2024-07-12 Shuichi Yokoyama

The hydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations is considered for weak solutions. Using relative entropy estimate about an absolute Maxwellian, an incompressible Electron-Magnetohydrodynamics-Fourier limit for solutions of…

Analysis of PDEs · Mathematics 2011-02-22 Xianpeng Hu , Dehua Wang

An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…

Numerical Analysis · Mathematics 2023-07-21 K. R. Arun , Rahuldev Ghorai , Mainak Kar

We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…

Analysis of PDEs · Mathematics 2020-05-26 Helge Kristian Jenssen , Charis Tsikkou

A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…

Fluid Dynamics · Physics 2024-02-23 Gui-Qiang G. Chen , James Glimm , Hamid Said

In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \cite{mixmodel} when the initial data is a small perturbation of global equilibrium. For this, we…

Analysis of PDEs · Mathematics 2022-01-06 Gi-Chan Bae , Christian Klingenberg , Marlies Pirner , Seok-Bae Yun

In this work a relation between topology and thermodynamical features of gravitational instantons is shown. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for the entropy of gravitational…

High Energy Physics - Theory · Physics 2011-09-09 Stefano Liberati , Giuseppe Pollifrone

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

Analysis of PDEs · Mathematics 2020-01-03 Eduard Feireisl , Martina Hofmanová

We consider solutions to the full (non-isentropic) two-dimensional Euler equations that are constant in time and along rays emanating from the origin. We prove that for a polytropic equation of state, entropy admissible solutions in…

Analysis of PDEs · Mathematics 2012-11-16 Joseph Roberts

We establish the incompressible low--Mach/high--Reynolds limit for the Boltzmann equation for a broad class of initial data, without recourse to any asymptotic expansion. Exploiting the local Maxwellian manifold and the macro--micro…

Analysis of PDEs · Mathematics 2026-04-07 Gi-Chan Bae , Chanwoo Kim

In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of…

Analysis of PDEs · Mathematics 2025-09-11 Geng Chen , Moon-Jin Kang , Alexis F. Vasseur

I calculate the hydrodynamic limit of the BGK approximation of the Boltzmann equation for the case of a long stress relaxation time and find that the stress obeys a viscoelastic constitutive equation. The constitutive equation is different…

Statistical Mechanics · Physics 2007-05-23 Alexander J. Wagner

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…

Statistical Mechanics · Physics 2008-11-26 Jörn Dunkel , Peter Talkner , Peter Hänggi

In this paper, we examine the question of the boundary controllability of the one-dimensional non-isentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian…

Optimization and Control · Mathematics 2013-04-16 Olivier Glass

We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…

Analysis of PDEs · Mathematics 2023-05-24 Hengrong Du , Yuanzhen Shao , Gieri Simonett