3 papers
math.FA2026
The trace-free Beurling--Ahlfors transform and the Bourgain--Brezis problem for Hodge systems
Diogo Arsénio
We show that the dual approach to Bourgain--Brezis estimates for Hodge systems is substantially more flexible than previously understood. For , we introduce the tr…
math.AP2024
Global unique solutions to the planar inhomogeneous Navier--Stokes--Maxwell equations
Diogo Arsénio, Haroune Houamed, Belkacem Said--Houari
The evolution of an electrically conducting imcompressible fluid with nonconstant density can be described by a set of equations combining the continuity, momentum and Maxwell's eq…
math.AP2024
Damped Strichartz estimates and the incompressible Euler--Maxwell system
Diogo Arsénio, Haroune Houamed
Euler--Maxwell systems describe the dynamics of inviscid plasmas. In this work, we consider an incompressible two-dimensional version of such systems and prove the existence and un…