Seminar talk, 23 September 2026

Speaker: Oleg Morozov

Title: A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations

Abstract:
I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and conservation laws of the system. Using the Lax representation, I will derive a shadow of a cosymmetry and find nonlocal conservation laws via the construction of the canonical conservation law on the Whitney sum of the tangent and cotangent coverings. Finally, I will present a Bäcklund transformation between the tangent and cotangent coverings and describe its action on local symmetries and local cosymmetries.

References:
arXiv:2409.05752