Qinghua Xiao

Bio: Qinghua Xiao is an academic researcher from Chinese Academy of Sciences. The author has contributed to research in topics: Riemann problem & Bessel function. The author has an hindex of 2, co-authored 3 publications receiving 10 citations.

Nonlinear Hyperbolic Waves in Relativistic Gases of Massive Particles with Synge Energy

Abstract: In this article, we study some fundamental properties of nonlinear waves and the Riemann problem of Euler’s relativistic system when the constitutive equation for energy is that of Synge for a monatomic rarefied gas or its generalization for diatomic gas. These constitutive equations are the only ones compatible with the relativistic kinetic theory for massive particles in the whole range from the classical to the ultra-relativistic regime. They involve modified Bessel functions of the second kind and this makes Euler’s relativistic system rather complex. Based on delicate estimates of the Bessel functions, we prove: (i) a limit on the speed of sound of $$1{/}\sqrt{3}$$ times the speed of light (which a fortiori implies subluminality, that is causality), (ii) the genuine non-linearity of the acoustic waves, (iii) the compatibility of Rankine–Hugoniot relations with the second law of thermodynamics (entropy growth through all Lax shocks), and (iv) the unique resolvability of the initial value problem of Riemann (if we include the possibility of vacuum as in the non-relativistic context).

The Riemann problem of relativistic Euler system with Synge energy

Abstract: In this paper, we study the Riemann problem of relativistic Euler system for rarefied monatomic and diatomic gases when the constitutive equation for the energy is the Synge equation that is the only one compatible with the relativistic kinetic theory. The Synge equation is involved with modified Bessel functions of the second kind and this makes the relativistic Euler system quite complex. Based on delicate estimates of the modified Bessel functions of the second kind, we provide a detailed investigation of basic hyperbolic properties and the structure of elementary waves, especially for the structure of shock waves and in this way, the mathematical theory of the Riemann problem for these relativistic Euler system, which is analogous to the corresponding theory of the classical ones, is rigorously provided.

Classical and ultrarelativistic limits of the Riemann problem for the relativistic Euler fluid with Synge energy

Abstract: Recently, Ruggeri et al. (The Riemann problem of relativistic Euler system with Synge energy, arXiv:2001.04128v1 [math-ph], 2020) studied the Riemann problem of the relativistic Euler system for rarefied monatomic and diatomic gases with a constitutive equation for the energy determined by Synge, which is the only realistic equation compatible with the kinetic theory. The aim of the present work is to consider the classical and ultrarelativistic limits of their results, showing that they are in agreement with those already present in literature.

Global Hilbert Expansion for the Relativistic Vlasov–Maxwell–Boltzmann System

Abstract: Consider the relativistic Vlasov–Maxwell–Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works Germain and Masmoudi (Ann Sci Ec Norm Super 47(3):469–503, 2014), Guo et al. (J Math Phys 55(12):123102, 2014) and Deng et al. (Arch Ration Mech Anal 225(2):771–871, 2017), we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler–Maxwell system as the mean free path goes to zero. Our method is based on the $$L^2-L^{\infty }$$ framework and the Glassey–Strauss Representation of the electromagnetic field, with auxiliary $$H^1$$ estimates and $$W^{1,\infty }$$ estimates to control the characteristic curves and corresponding $$L^{\infty }$$ norm.

On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections

Abstract: A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-paramete...

On a relativistic BGK model for polyatomic gases near equilibrium

Abstract: Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting model and Marle this http URL this paper, we prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.