Related papers: Perturbative variational formulation of the Vlasov…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas…
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lema\^itre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy…
The goal of this article is to give a formal derivation of Ohm's law of Magnetohydrodynamics (MHD) starting from the Vlasov-Maxwell-Boltzmann system. The derivation is based on various physical scalings and the moment methods when the…
The Vlasov-Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation ("lift") of the Vlasov-Maxwell bracket induced by the dynamical…
Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity ${\bf \Omega}$ and magnetic…
Onsager and Machlup proposed a second order variational-principle in order to include inertial effects into the Langevin-equation, giving a Lagrangian with second order derivatives in time. This but violates Ostrogradysky's theorem, which…
Hydrodynamic equations for an inelastic Maxwell model are derived from the inelastic Boltzmann equation based on a systematic Chapman-Enskog perturbative scheme. Transport coefficients appear in Navier-Stokes order have been determined as a…
Variational principle is the main approach to obtain complete and self-consistent field equations in gravitational theories. This method works well in pure field cases such as $f(R)$ and Horndeski gravities. However, debates exist in the…
New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational…
We present a systematic theoretical framework for investigating first-order electromagnetic (EM) perturbations induced by gravitational waves (GWs). Beginning with the covariant Maxwell equations, we derive the complete first-order…
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were…
We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid…
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove pathwise global existence, uniqueness, and temporal…
Based on the Newton's second law and the Maxwell equations for the electromagnetic fields, we establish a new 3D incompressible magneto-hydrodynamics(MHD) equations for the motion of plasma under the standard Coulomb gauge. By using the…
We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…
The Cauchy problem for the Vlasov-Maxwell-Boltzmann equations (VMB) is considered. First the renormalized solution to the Vlasov equation with the Lorentz force is discussed and the difficulty on the partial differentiability of the…
The algebra of invariants for both the relativistic and nonrelativistic multispecies Vlasov-Maxwell system is examined, including the case with a fixed ion background. Invariants and their associated fluxes are obtained directly from the…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
Except for the presence of gravitational wave source term, the relativistic perturbation equations of a zero-pressure irrotational fluid in a flat Friedmann world model coincide exactly with the Newtonian ones to the second order in…