On Some Properties of Trajectories of Non-Smooth Vector Fields

Victor Zvyagin (), Vladimir Orlov and Andrey Zvyagin
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Victor Zvyagin: Mathematical Department, Voronezh State University, 394018 Voronezh, Russia
Vladimir Orlov: Mathematical Department, Voronezh State University, 394018 Voronezh, Russia
Andrey Zvyagin: Mathematical Department, Voronezh State University, 394018 Voronezh, Russia

Mathematics, 2024, vol. 12, issue 11, 1-18

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.

Keywords: systems of ordinary differential equations; Cauchy problems; multi-connected domain; Sobolev space; viscoelastic continuous medium; inhomogeneous conditions; regular Lagrangian flow (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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