Differential equations with singular fields

Pierre-Emmanuel Jabin (1, 2)

1 TOSCA - Simuler et calibrer des modèles stochastiques
2 JAD - Laboratoire Jean Alexandre Dieudonné

This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the vector field, a compressibility condition on the flow (bounded Jacobian) is considered. The main result provides existence under the condition that the vector field belongs to BV in dimension 2 and SBV in higher dimensions.

Mots clés: ODE's; Singular forces; Stability estimates

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]

Pierre-Emmanuel Jabin. Differential equations with singular fields. Journal de Mathématiques Pures et Appliquées, 2010, 94 (6), pp.597-621. ⟨10.1016/j.matpur.2010.07.001⟩. ⟨hal-00601959⟩