相关论文: The Newtonian limit of the relativistic Boltzmann …
We build a minimal extension of General Relativity in which Newton's gravitational coupling, $G$, the speed of light, $c$, and the cosmological constant, $\Lambda$, are spacetime variables. This is done while satisfying the contracted…
In this paper, we prove the global existence and uniqueness of mild solution to the relativistic Boltzmann equation both in the whole space and in torus for a class of initial data with bounded velocity-weighted $L^\infty$-norm and some…
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the regularity of both dynamical and steady Boltzmann equation in strictly convex domain with the Cercignani-Lampis…
It has been known that dimensional constants such as $\hbar$, $c$, $G$, $e$, and $k$ are merely human constructs whose values and units vary depending on the chosen system of measurement. Therefore, the time variation of dimensional…
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the…
A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity…
We present empirical evidence extracted directly from the Pantheon Catalog of SNeIa demonstrating that the speed of light varies as the universe expands. Moreover, the speed of light must vary in a specific quantifiable manner. To show…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal…
A stationary line element of general relativity seems to be compatible to essential cosmological facts (though only as far as one can expect solving the nonlinear Einstein equations neglecting local cosmic evolution and all spatial…
In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox is provided. The presented approach reveals the connection between…
We study the uniqueness and regularity of the steady states of the diffusively driven Boltzmann equation in the physically relevant case where the restitution coefficient depends on the impact velocity including, in particular, the case of…
Following the basic idea expressed in [1], we assume that for any particle or body with mass M its own time t depends on therelative change \frac{\Delta M}{M} of that mass. Based on this assumption, one discusses possible existence of a…
We consider a system of particles subjected to a uniform external force E and undergoing random collisions with "virtual" fixed obstacles, as in the Drude model of conductivity. The system is maintained in a nonequilibrium stationary state…
By exploring the relationship between the propagation of electromagnetic waves in a gravitational field and the light propagation in a refractive medium, it is shown that, in the presence of a positive cosmological constant, the velocity of…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
The varying speed of light theories have been recently proposed to solve the standard model problems and anomalies in the ultra high energy cosmic rays. These theories try to formulate a new relativity with no assumptions about the…