Year: 2010
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Jabin, Pierre-Emmanuel
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952812292