Chillan Workshop in Applied Mathematics CWAM 2023

Regularity criteria for 3D MHD flows in terms of spectral components

12 Jan 2023, 17:00

1h

Campus Fernando May, UBB (Chillan)

Speaker

Eduardo Notte Cuello (DMAT ULS)

Description

We extend the spectral regularity criteria of the Prodi-Serrin kind for the Navier-Stokes
equations in a torus to the MHD equations. More precisely, the following is established: for any N > 0, let x_N and y_N be the sum of all spectral components of the velocity and magnetic field whose wave numbers possess absolute value greater that N; then, it is possible to show that for any N the finiteness of the Prodi-Serrin norm of x N implies the regularity of the weak solution (u, h); thus, no restriction on the magnetic field is needed.