Global Existence of a Weak Solution of the Incompressible Euler Equations with Helical Symmetry and L-p Vorticity

Author(s)

Bronzi, A. C. ^[1] ; Lopes Filho, M. C. ^[2] ; Nussenzveig Lopes, H. J. ^[2]

Affiliation

^[1] Univ Estadual Campinas, Inst Matemat Estat & Computacao Cient, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ - Brazil

• Document type: Journal article
• Source: Indiana University Mathematics Journal; v. 64, n. 1, p. 309-341, 2015.
• Web of Science Citations: 4

Abstract

We prove the global existence of a helical weak solution of the 3D Euler equations, in full space, for an initial velocity with helical symmetry, without swirl, and whose initial vorticity is compactly supported in the axial plane and belongs to L-p, for some p > 4/3. This result is an extension of the existence part of the work of B. Ettinger and E. Titi {[}9], who studied well-posedness of the Euler equations with helical symmetry without swirl, with bounded initial vorticity, in a helical pipe. (AU)

• FAPESP's process: 07/51490-7 - Mathematical aspects of incompressible fluid dynamics
• Grantee: Milton da Costa Lopes Filho
• Support Opportunities: Research Projects - Thematic Grants