Vlasov-Poisson equations for a two-component plasma in a homogeneous magnetic field

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.…”

Nonlocal elliptic problems in infinite cylinder and applications

“…Here P : C σ 0 (Q) → C 2+σ 0 (Q) is a linear bounded operator. In [26], it was proved the following statement.…”

“…We consider the Vlasov-Poisson equations in infinite cylinder with nonlocal boundary condition for the electric field potential and initial conditions for density distribution functions of charged particles. Applying Theorem 6.3 on a unique solvability of nonlocal elliptic problems in a cylinder in Hölder spaces and Theorem 5.1 in [26] on solvability of abstract Vlasov equations, we prove that there is a unique classical solution of the above problem for sufficiently small initial density distribution functions. Moreover, the supports of density distribution functions belong to some interior cylinder.…”

Confined steady states of a Vlasov‐Poisson plasma in an infinitely long cylinder

“…For the three-dimensional Vlasov-Poisson system, steady states of that type have already been investigated by Skubachevskii. 1 Here, for the two-dimensional system, only slight modifications to his approach are necessary. We assume that b ≡ for some constant > 0.…”