Some remarks on the continuity equation
Patrick Bernard (CEREMADE)
TL;DR
This paper explores the relationship between the properties of the initial value problem for ordinary differential equations and the associated continuity equation in measure spaces, highlighting their interconnected behaviors.
Contribution
It provides new insights into how the properties of ODEs influence the solutions of the continuity equation in the context of measures.
Findings
Established links between ODE Cauchy problem and measure-based continuity equation
Identified conditions under which properties of solutions are preserved
Enhanced understanding of measure-theoretic aspects of continuity equations
Abstract
We describe some relations between the properties of the Cauchy problem for an ODE and the properties of the Cauchy problem for the associated continuity equation in the class of measures.
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Taxonomy
TopicsAdvanced Banach Space Theory · Stability and Controllability of Differential Equations · Navier-Stokes equation solutions