The Riemann problem of relativistic Euler system with Synge energy

Lagrangians with linear velocities within Riemann-Liouville fractional derivatives

Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the recovery of the classical results was discussed.

关于由欧拉系统得到的里曼波叠加的分析

On Riemann wave superpositions obtained from the Euler system

本文通过分析欧拉系统中的波叠加条件，引入准可测性概念，并构造了描述波叠加行为的无限维李代数，进而推导出非弹性波叠加区域的参数化形式。

物理类中黎曼激波的稳定性：从Brenner-Navier-Stokes-Fourier到Euler

Stability of a Riemann Shock in a Physical Class: From Brenner-Navier-Stokes-Fourier to Euler

该研究针对Euler系统黎曼激波无条件稳定性的开放问题，以Brenner-Navier-Stokes-Fourier系统为物理粘性模型，通过改进带位移的a-收缩方法证明了小振幅黎曼激波在耗散消失极限下的稳定唯一性，首次解决了该类问题。

Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases

We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit the concentration of mass. It is found that, under the requirement of satisfying the over-compressing entropy condition: (i) there is a unique delta shock solution, corresponding to the case that has two strong classical Lax shocks; (ii) for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave, or two shocks with one being weak, there are infinitely many solutions, each consists of a delta shock and a …

势流 Euler 方程四激波相互作用二维 Riemann 问题的全局解

Global Solutions of the Two-Dimensional Riemann Problem with Four-Shock Interactions for the Euler Equations for Potential Flow

本文提出严格方法构造势流 Euler 方程四激波相互作用二维 Riemann 问题的全局解，通过引入三个临界角并转化为混合型方程自由边界问题，首次给出该问题的严格理论结果。

The Euler-Riemann Gases, and Partition Identities

The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice ($s$-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order $s$ of the parafermions. It is also shown that these pa…

On the global regularity of sub-critical Euler-Poisson equations with pressure

We prove that the one-dimensional Euler-Poisson system driven by the Poisson forcing together with the usual γ-law pressure, γ ≥ 1, admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the 2x2 p-system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold.

轴对称3-D Euler方程的Zeitlin模型

Zeitlin's model for axisymmetric 3-D Euler equations

本文将Zeitlin模型扩展至3-球面上的轴对称Euler方程，首次提出完全保留几何结构的3-D Euler方程有限维离散化，并讨论了其黎曼曲率与Jacobi方程。

On universality of homogeneous Euler equation

Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type equations. Integrable one dimensional systems in terms of Riemann invariants and its extensions, multidimensional equations describing isoenthalpic and polytropic motions and shallow water type equations are among them.

The Euler and Navier-Stokes equations on the hyperbolic plane

We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on the hyperbolic spaces of higher dimension. We also describe the corresponding general Hamiltonian setting of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.