4 papers
Global well-posedness of the 3D Navier-Stokes equations with helical vorticity
Francisco Gancedo, Antonio Hidalgo-Torné
We show that the Navier-Stokes equations on are globally well posed for initial vorticities that are both helically symmetric and integrable. This clas…
Pathological solutions of Navier-Stokes equations on with gradients in Hardy spaces
Jan Burczak, Antonio Hidalgo-Torné
For an arbitrary smooth initial datum, we construct multiple nonzero solutions to the d Navier-Stokes equations, with their gradients in the Hardy space with any…
Dissipative Euler flows originating from circular vortex filaments
Francisco Gancedo, Antonio Hidalgo-Torné, Francisco Mengual
In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in $C([0,T],L^{2^-}…
On the Cauchy problem for 3D Navier-Stokes helical vortex filament
Francisco Gancedo, Antonio Hidalgo-Torné
This paper studies the Cauchy problem for a helical vortex filament evolving by the 3D incompressible Navier-Stokes equations. We prove global-in-time well-posedness and smoothing…