Related papers: Shock wave formation in Rosenau's extended hydrody…
The effects arising from accelerated and decelerated motion of a point charge inside a medium are studied. The motion is manifestly relativistic and may be produced by a constant uniform electric field. It is shown that in addition to the…
We analyze a recent experiment [Phys. Rev. Lett., {\bf103}, 224501 (2009)] in which the shock, created by the impact of a steel ball on a flowing monolayer of glass beads, is quantitatively studied. We argue that radial momentum is…
We present a criterion for a shock wave existence in relativistic magnetic hydrodynamics with an arbitrary (possibly non-convex) equation of state. The criterion has the form of algebraic inequality that involves equation of state of the…
Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional…
For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and…
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long"…
In this work we revisit the topic of existence of hydrodynamic shock waves in a cold weakly collisional plasma. For this purpose we consider the well established Adlam-Allen model with the addition of a dashpot term associated with the…
The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca,…
Starting from coupled fluid-kinetic equations for the modeling of laden flows, we derive relevant viscous corrections to be added to asymptotic hydrodynamic systems, by means of Chapman-Enskog expansions and analyse the shock profile…
Linear stability of a plane shock waves in ultrarelativistic anisotropic hydrodynamics is investigated. The properties of the amplitudes of perturbations of physical quantities are studied depending on the components of the wave vector of a…
We extend the reactive Burgers equation presented in Kasimov et al. Phys. Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to include multidimensional effects. Furthermore, we explain how the model can be rationally…
We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…
In this paper, we prove the finite-time shock formation for the compressible Euler equations on the two-dimensional sphere $\mathbb{S}^2$. In contrast to the flat Euclidean case $\mathbb{R}^2$, the geometry of $\mathbb S^2$ imposes new…
The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form…
The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This…
Extended theories are widely used in the literature to describe relativistic fluids. The motivation for this is mostly due to the causality issues allegedly present in the first order in the gradients theories. However, the decay of…
Extended Self-Similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier--Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained.…
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, including the rates at which the local extrema converge to the…
We use the one-dimensional steady version of the equations derived in paper I to compute the structure of shock waves. The agreement with experiment is good, especially when we retain the experimental value of the Prandtl number adopted in…
The shallow-water system is a standard model for long waves in shallow water. The system is hyperbolic and, for a large class of initial data, solutions develop steep gradients leading to shock formation in finite time. Since such…