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On Some Properties of Trajectories of Non-Smooth Vector Fields

Author

Listed:
  • Victor Zvyagin

    (Mathematical Department, Voronezh State University, 394018 Voronezh, Russia
    These authors contributed equally to this work.)

  • Vladimir Orlov

    (Mathematical Department, Voronezh State University, 394018 Voronezh, Russia
    These authors contributed equally to this work.)

  • Andrey Zvyagin

    (Mathematical Department, Voronezh State University, 394018 Voronezh, Russia
    These authors contributed equally to this work.)

Abstract

In this paper, we study the properties of trajectories of systems of ordinary differential equations generated by the velocity field of a moving incompressible viscoelastic fluid with memory along the trajectories in a domain with multiple boundary components. The case of a velocity field from a Sobolev space with inhomogeneous boundary conditions is considered. The properties of the maximal intervals of existence of solutions to the Cauchy problem corresponding to a given velocity field are investigated. The study assumes the approximation of a velocity field by a sequence of smooth fields followed by a passage to the limit. The theory of regular Lagrangian flows is used.

Suggested Citation

  • Victor Zvyagin & Vladimir Orlov & Andrey Zvyagin, 2024. "On Some Properties of Trajectories of Non-Smooth Vector Fields," Mathematics, MDPI, vol. 12(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1703-:d:1405647
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