Propagation of singularities by Osgood vector fields and for 2D inviscid incompressible fluids

• Published in: Mathematische annalen Vol. 387; no. 3-4; pp. 1691 - 1718
• Main Authors: Drivas, Theodore D., Elgindi, Tarek M., La, Joonhyun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V
• Subjects: Euler-Lagrange equation; Fields (mathematics); Fluid flow; Incompressible flow; Incompressible fluids; Mathematics; Mathematics and Statistics; Perturbation; Singularity (mathematics); Velocity distribution
• ISSN: 0025-5831; 1432-1807
• DOI: 10.1007/s00208-022-02498-2

We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure of these singularities is related to the modulus of continuity of the velocity and the results are shown to be sharp in t...