Related papers: The Vlasov equation cannot fully account for colli…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…
A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…
In this paper we study the general relationship between the evolutionary conditions for discontinuous solutions of hyperbolic conservation laws with a concave entropy function and the existence and uniqueness of steady dissipative shock…
An exact solution of the collisionless time-dependent Vlasov equation is found for the first time. By means of this solution the behavior of the Langmuir waves in the nonlinear stage is considered. The analysis is restricted by the…
The Vlasov system of equations for a plasma is given in relativistic form, and using the correct expression for the "Lorentz" force, that is the one guaranteing real self-consistency.
We consider the Vlasov-Poisson equation in $\mathbb{R}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we…
We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact…
Despite being studied for many years, the structure of collisionless shocks is still not fully determined. Such shocks are known to be accelerators of cosmic rays, which, in turn, modify the shock structure. The shock width $\lambda$ is…
This paper is devoted to consideration of the theory of collisionless statistical systems with interparticle scalar interaction. The mathematical model of such systems is constructed and the exact solution of Vlasov equation for isotropic…
For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by supplementing the equations with a kinetic relation…
We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…
In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly…
In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks…
Collisionless shocks in plasmas play an important role in space physics (Earth's bow shock) and astrophysics (supernova remnants, relativistic jets, gamma-ray bursts, high energy cosmic rays). While the formation of a fluid shock through…
A collisionless plasma is modeled by the Vlasov-Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as x tends to…
A direct numerical simulation of a strong relativistic collisionless shock propagating into an unmagnetized medium has been performed in two spatial dimensions. It is found that: (i) collisionless shock exists, (ii) particle acceleration is…
This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic i.e. non-idealized plasmas. Above all, this means giving up the well-known concept of a linear wave theory in favor of a thoroughly…
We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…