耗散双流体模型

On Shock Profiles in Four-Field Formulations of Dissipative Relativistic Fluid Dynamics

This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors' earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativistic dynamics of barotropic fluids in the presence of viscosity and heat conduction, shock waves of arbitrary strength have smooth, monotone dissipation profiles. The results and arguments extend classical considerations of Weyl (Comm. Pure Appl. Math. 2 (1949)) and Gilbarg (Amer. J. Math. 73 (1951)) to the relativistic setting.

变分法在一般耗散流体系统中的应用：微分形式

Variational formulation of a general dissipative fluid system with differential forms

本文通过几何变分法研究耗散流体系统，引入任意数量的微分形式变量，统一了耗散源、热力学通量闭合及其边界条件，满足热力学基本定律，并重新审视Curie原理。

相对论耗散流体力学Landau-Lifshitz能量框架的唯一性

Uniqueness of Landau-Lifshitz Energy Frame in Relativistic Dissipative Hydrodynamics

我们表明，相对论性耗散流体动力学方程从相对论性玻尔兹曼方程的重整化群方法唯一导致的能量框架中提出的朗道和Lifshitz，提供的宏观框架矢量，它定义了当地的静止框架的流体速度，是独立的组成粒子的动量，因为它应该。我们认为，粘性流体的相对论流体动力学方程必须定义在能量框架上，如果它是一致的相对论动力学方程。

On a class of generalized solutions to equations describing incompressible viscous fluids

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by the measure-valued solutions for the inviscid (Euler) system. We show the existence as well as the weak-strong uniqueness property in the class of dissipative solutions. Finally, the dissipative solution enjoying certain extra regularity coincides with a strong solution of the same problem.

耗散流体动力学的协变action原理：从形式主义到基础物理

A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics

提出了一种新的耗散广义相对论流体动力学变分框架。该模型扩展了对流变分原理的多流体系统，占范围内的耗散通道。构造中的关键成分是：i）对每个流体组分使用低维物质空间，以及ii）相关体积形式的扩展函数依赖性。为了使概念清晰，形式主义是在每一个层次上考虑的物质耦合到热的模型例子的步骤。因此，我们讨论一个模型的热流，推导出相对论性的纳维-斯托克斯方程和讨论为什么个别的耗散应力张量不需要时空对称。我们认为，新的形式主义，这显然不涉及从一个假定的平衡态的扩展，提供了一个概念上的突破，在这一领域的研究，并提供了一个雄心勃勃的方向清单，其中一个可能要扩展它在未来。这涉及到一系列令人兴奋的问题，涉及到应用和基础问题。

在具有几何修正的紧凑流体域中研究耗散涡二元组

Dissipative Vortex Binaries in Compact Fluid Domains with Geometric Corrections

本文研究了在双周期流体域中耗散涡二元组的动力学，通过最小旋转速度项引入耗散，揭示了哈密顿结构、耗散和几何在周期性流体系统中的相互作用。

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade…

Effective field theory of dissipative fluids

We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal de…

Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current

In this paper we further develop the fluctuating hydrodynamics proposed in arXiv:1511.03646 in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a $Z_2$ symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physica…