4 papers
Existence of hyperbolic blow-up to the generalized quasi-geostrophic equation
Lucas C. F. Ferreira, Ricardo M. M. Guimarães
In this work, we investigate the blow-up of solutions to the generalized surface quasi-geostrophic (gSQG) equation in , within the more singular range f…
On the Helmholtz decomposition in Morrey and block spaces
Lucas C. F. Ferreira, Marcos G. Santana
In this work, we obtain the Helmholtz decomposition for vector fields in Morrey, Zorko, and block spaces over bounded or exterior domains. Generally speaking, our proofs re…
Dispersive estimates and generalized Boussinesq equation on hyperbolic spaces with rough initial data
Lucas C. F. Ferreira, Pham T. Xuan
We consider the generalized Boussinesq (GBq) equation on the real hyperbolic space () in a rough framework based on Lorentz spaces. First, we establish dis…
On the well-posedness of the Hall-MHD system in a critical setting of Besov-Morrey type
Lucas C. F. Ferreira, Rafael P. da Silva
In this paper, we address the 3D incompressible Hall-magnetohydrodynamic system (Hall-MHD). Our objective is to provide local and global well-posedness results for initial velocity…