Non-Uniqueness and prescribed energy for the continuity equation
Gianluca Crippa, Nikolay Gusev, Stefano Spirito, Emil Wiedemann
TL;DR
This paper demonstrates the non-uniqueness of solutions to the continuity equation by constructing infinitely many weak solutions with a specified energy, challenging assumptions of uniqueness.
Contribution
It introduces new non-uniqueness examples for the continuity equation through the construction of infinitely many weak solutions with prescribed energy.
Findings
Existence of infinitely many weak solutions with the same energy
Non-uniqueness of solutions to the continuity equation
Method for constructing solutions with prescribed energy
Abstract
In this note we provide new non-uniqueness examples for the continuity equation by constructing infinitely many weak solutions with prescribed energy.
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