相关论文: On the density of "wild" initial data for the baro…

The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense $G_\delta$ set of initial data, the solutions lose regularity in infinite time,…

The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor.…

In this paper, we consider diagonal hyperbolic systems with monotone continuous initial data. We propose a natural semi-explicit and upwind first order scheme. Under a certain non-negativity condition on the Jacobian matrix of the…

In this paper, we study the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional bounded simply…

The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…

We propose new construction of dependent variables for equations of an ideal barotropic fluid. This construction is based on a direct generalization of the known connection between Schroedinger equation and a system of Euler-type equations.…

We consider front tracking approximate solutions to the p-system of isentropic gas dynamics. At interaction times, the outgoing wave fronts have the same strength as in the exact solution of the Riemann problem, but some error is allowed in…

In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…

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…

We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy…

It is shown that if (M,phi,alpha) is a W*-dynamical system with M a type I von Neumann algebra then the entropy of alpha w.r.t. phi equals the entropy of the restriction of alpha to the center of M. If furthermore (N,psi,beta) is a…

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is…

We show that for every linear toral automorphism, especially the non-hyperbolic ones, the entropies of ergodic measures form a dense set on the interval from zero to the topological entropy.

In this article our goal is to study the singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $=\epsilon^m $, Rossby number $=\epsilon $ and Froude number $=\epsilon^n…

We investigate the role of entropic concepts for the relaxation dynamics in granular systems. In these systems the existence of a geometrical frustration induces a drastic modification of the allowed phase space, which in its turn induces a…

We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method.…

The question of what is the total entropy of the universe, how it compares to the maximal entropy of de Sitter space, and how it is distributed across the universe's components, bears considerable importance for a number of reasons. Here,…

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…

The fundamental information-theoretic measures (the R\'enyi $R_{p}[\rho]$ and Tsallis $T_{p}[\rho]$ entropies, $p>0$) of the highly-excited (Rydberg) quantum states of the $D$-dimensional ($D>1$) hydrogenic systems, which include the…