Hydrodynamic Coherence and Vortex Solutions of the Euler–Helmholtz Equation

The form of the general solution of the steady-state Euler–Helmholtz equation (reducible to the Joyce–Montgomery one) in arbitrary domains on the plane is considered. This equation describes the dynamics of vortex hydrodynamic structures.     

S.K. Godunov and Kinetic Theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Computational Mathematics and Mathematical Physics - The history of the cooperation between the staff of the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences and S.K....     

Equation of Vlasov–Maxwell–Einstein Type and Transition to a Weakly Relativistic Approximation

Computational Mathematics and Mathematical Physics - The gravitational Lagrangian of general relativity is considered together with the Lagrangian of electromagnetism. Vlasov-type equations are...     

Application of the Kac equation to turbulence simulation

The possibility of applying the Kac equation to the simulation of small-scale turbulence is explored. The hypothesis is substantiated that the formation of a flow regime similar to the actual turbulent one can be qualitatively described as based on the analysis of the properties of the Kac equation.     

Simulation of collisionless ultrarelativistic electron–proton plasma dynamics in a self-consistent electromagnetic field

The evolution of a collisionless electron–proton plasma in the self-consistent approximation is investigated. The plasma is assumed to move initially as a whole in a vacuum with the Lorentz factor. The behavior of the dynamical system is analyzed by applying a three-dimensional model based on the Vlasov–Maxwell equations with allowance for retarded potentials. It is shown that the analysis of the solution to the problem is not valid in the “center-of-mass frame” of the plasmoid (since it cannot be correctly defined for a relativistic plasma interacting via an electromagnetic field) and the transition to a laboratory frame of reference is required. In the course of problem solving, a chaotic electromagnetic field is generated by the plasma particles. As a result, the particle distribution functions in the phase space change substantially and differ from their Maxwell–Juttner form. Computations show that the kinetic energies of the electron and proton components and the energy of the self-consistent electromagnetic field become identical. A tendency to the isotropization of the particle momentum distribution in the direction of the initial plasmoid motion is observed.     

Branching of Solutions of the Abstract Kinetic Equation

In this paper, bifurcation of solutions of a special nonlinear operator equation used in mathematical physics is considered. In the case of an equation for which the Fréchet derivative of the associated operator is a locally perturbed Fredholm operator, sufficient conditions for branching of solutions are studied. The methodology of application of the formalism developed in the paper is demonstrated by the example of the Boltzmann equation.     

Numerical simulation of inviscid bubble dynamics in a centrally symmetric gravitational field

The motion of bubbles in a centrally symmetric gravitational field is numerically simulated using two-dimensional conservation laws (Euler equations). The dynamics of bubbles with various numbers of modes in the initial perturbation are studied. The numerical results reveal features that are substantially different from the plane case in a homogeneous gravitational field. Bubble perturbations nearly do not interact at the formation stage. The lowest modes are amplified in the course of the bubble evolution.     

Possibility of explaining the existence of vortexlike hydrodynamic structures based on the theory of stationary kinetic equations

The possibility of describing vortex structures in quasi-one-dimensional plane flows by applying kinetic equations and bifurcation theory is examined. The Lyapunov-Schmidt method is used to obtain a system of Riccati-type generalized bifurcation equations. An analysis of its properties leads to conditions for the existence of vortex structures.