Abstract
The aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags, which can been viewed as an infinite dimensional system of first-order conservation laws. The waterbag model, which constitutes a special class of exact weak solution of the Vlasov equation, is well known in plasma physics, and its applications in gyrokinetic theory and laser–plasma interaction are very promising. The proof of the existence of a continuum of regular waterbags relies on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations, some results in singular integral operators theory and harmonic analysis, Riemann–Hilbert boundary value problems and energy estimates.
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Besse, N. On the Waterbag Continuum. Arch Rational Mech Anal 199, 453–491 (2011). https://doi.org/10.1007/s00205-010-0392-9
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DOI: https://doi.org/10.1007/s00205-010-0392-9