Global solutions for the one dimensional Water-Bag model

Mihai Bostan (1, 2) , Jose Antonio Carrillo (3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 CALVI - Scientific computation and visualization
3 UAB - Departament de Matemàtiques [Barcelona]

In this paper we study a special type of solution for the one dimensional Vlasov-Maxwell equations. We assume that initially the particle density is constant on its support in the phase space and we are looking for solutions with particle density having the same property at any time t > 0. More precisely, for each x the support of the density is assumed to be an interval [p,P] with end-points varying in space and time. We analyze here the case of weak and strong solutions for the effective equations verified by the end-points and the electric field (water-bag model) in the relativistic setting.

Mots clés: Vlasov-Maxwell equations; water-bag model; conservation laws

Domaines: Equations aux dérivées partielles [math.AP]; Physique des plasmas [physics.plasm-ph]

Mihai Bostan, Jose Antonio Carrillo. Global solutions for the one dimensional Water-Bag model. Communications in Mathematical Sciences, 2009, 7 (1), pp.129-141. ⟨10.4310/CMS.2009.v7.n1.a6⟩. ⟨hal-00594958⟩