Differential equations with singular fields

By Pierre-Emmanuel Jabin. 2010

53 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e90e496624ae5c384586fa65cdc7e26c4e7fa9ed

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Lagrangian flows for vector fields with gradient given by a singular integral (2012, background): “10) contains the regularity W 1,1 (take K = δ0), already considered in [20] (see also [12]).”
Continuity equations and ODE flows with non-smooth velocity* (2014, background): “Some related analysis, with further developments in the case of kinetic equations, is contained in [81, 54].”
Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor (2015, background): “Proof A full proof of such well known result can for instance be found in [43] in a more general setting namely u ∈ BV .”