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On the waterbag continuum. (English) Zbl 1229.35297

A Vlasov type equation on a period interval (modelling a one-dimensional periodic plasma) is studied with regards to a special class of exact weak solutions known as the waterbag model. Existence of a continuum of regular waterbags is shown. The proof is based on a-priori estimates of terms associated with Riemann invariants and uses harmonic analysis, Riemann-Hilbert boundary value solution theory and singular integral operators.

MSC:

35Q83 Vlasov equations
45K05 Integro-partial differential equations
76X05 Ionized gas flow in electromagnetic fields; plasmic flow

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