Non-Uniqueness in Plane Fluid Flows
Abstract
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point produces an infinite number of solutions with the same initial data. Dafermos appeals to a maximal entropy rate criterion to recover uniqueness. These results are here interpreted as non-unique Lagrange trajectories on a particular spatial region. The corresponding velocity is proved consistent with plane steady compressible fluid flows that for specified pressure and mass density satisfy not only the Euler equations but also the Navier-Stokes equations for specially chosen volume and (positive) shear viscosities. The maximal entropy rate criterion recovers uniqueness.
Cite
@article{arxiv.2301.09122,
title = {Non-Uniqueness in Plane Fluid Flows},
author = {Heiko Gimperlein and Michael Grinfeld and Robin J. Knops and Marshall Slemrod},
journal= {arXiv preprint arXiv:2301.09122},
year = {2024}
}
Comments
25 pages, 10 figures, to appear in Quarterly of Applied Mathematics