Stationary Solutions of the Vlasov Equations for a High-Temperature Two-Component Plasma

Vlasov-Maxwell-Einstein Equation and Einstein Lambda

“…It seems promising to research all classical substitutions for this equation that are well-known for the Vlasov equation: energy and hydrodynamic ones [6][7][8][9]. It's also interesting to investigate the stationary solutions [18][19][20][21][22][23][24][25]. The problem of classifying all time-dependent (spatially homogeneous) solutions is relevant and interesting too, because it leads to cosmological solutions, which are now being actively studied.…”

Stationary solutions of the Vlasov–Poisson system for two-component plasma under an external magnetic field in a half-space

“…We would like to emphasize that solutions constructed in [4,8] and in Section 3 of this paper do not depend on x 3 . This fact can be interpreted in such a way that the plasma has an infinite mass.…”

“…We make the change of variables y = eh c x and w = eh c (p 2 , −p 1 , −p 3 ). Then using the equalities 2,3,4,5) and defining x = c eh (−y 1 , −y 2 , y 3 ) and p = c eh (−w 2 , w 1 , −w 3 ), we find that…”

“…Depending on the initial physical models, one distinguishes the Vlasov-Poisson equations, the Vlasov-Maxwell equations, the Vlasov-Einstein equations, the generalized Vlasov equations, and so on. There is an extensive literature on the Vlasov equations (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the references given there).…”

“…Note that in [6][7][8][9][10][11] the influence of an external magnetic field on the trajectories of particles was considered. In [4,8] there was constructed a stationary solution for which the charged-particle density distributions were supported in a strictly interior cylinder. It was shown that a classical solution for which the supports of the charged-particle density distributions are at a distance from the cylindrical boundary exists and is unique in some neighbourhood of the stationary solution [8].…”