Abstract
Complete mathematical description on plasmas contains not only some coupled partial differential equations (PDEs) reflecting physics laws but also some inequalities reflecting physical reasonableness requirement. The phrase ‘physical reasonableness’ refers to that solutions should always correspond to non-negative-valued probability distribution function and non-negative-valued particle density. This work displays a universal strict method on the V-M system with a constraint inequality f ≥ 0∀ r, p, t. It treats the Vlasov equation as a recurrence formula relating expansion coefficient functions of the power series solution of the equation, and strictly demonstrates that the constraint determines the shape, or geometric characteristics, of space-time contours of the fluid velocity field. Consequently, the constraint inequality makes those PDEs reflecting physics laws to be expressed finally as an ordinary equation of the fluid velocity field with respect to its contour.
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