6 papers
Bifurcation and global continuation of travelling-rotating Schrödinger maps on the sphere
Juan Carlos Sampedro, Luis Vega
We study travelling-rotating solutions of the Schrödinger map equation into the sphere, viewed as tangent profiles of rigid vortex filaments. Two first integrals reduce the profil…
On low regularity well-posedness of the binormal flow
Valeria Banica, Renato LucÃ, Nikolay Tzvetkov +1
We focus on a class of solutions of the binormal flow, model of the evolution of vortex filaments, that generate several corner singularities in finite time. This phenomenon has be…
A theorem concerning Fourier transforms: A survey
Aingeru Fernández-Bertolin, Luis Vega
In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic ana…
Multifractality and intermittency in the limit evolution of polygonal vortex filaments
Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod +1
With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functi…
Turbulent solutions of the binormal flow and the 1D cubic Schrödinger equation
Valeria Banica, Luis Vega
In the last three decades there has been an intense activity on the exploration of turbulent phenomena of dispersive equations, as for instance the growth of Sobolev norms since th…
Multifractality and polygonal vortex filaments
Valeria Banica, Daniel Eceizabarrena, Andrea. R. Nahmod +1
In this proceedings article we survey the results in [5] and their motivation, as presented at the 50th Journées EDP 2024. With the aim of quantifying turbulent behaviors of vorte…