Differential Equations with singular fields

Abstract

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.

References in corpus (2)

• An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions
• A Lemma and a Conjecture on the Cost of Rearrangements