5 papers · 1 filter
On bilinear estimates and critical uniqueness classes for Navier-Stokes equations
Lucas C. F. Ferreira, Jhean E. Pérez-López, Julio C. Valencia-Guevara
We are concerned with bilinear estimates and uniqueness of mild solutions for the Navier-Stokes equations in critical spaces. For that, we construct general settings in which estim…
On the Convergence of the JKO-scheme and Blow-up of solutions for a Multi-species Chemotaxis System with no Mass Preservation
Julio C. Valencia-Guevara
This work considers a chemotaxis system for multi-species that includes birth or death rate terms, which implies no mass preservation of the populations. We aim to show the converg…
Minimizing Movement for a Fractional Porous Medium Equation in a Periodic Setting
Lucas C. F. Ferreira, Matheus C. Santos, Julio C. Valencia-Guevara
We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability mea…
Gradient flows of time-dependent functionals in metric spaces and applications for PDEs
Lucas C. F. Ferreira, Julio C. Valencia-Guevara
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditi…
Periodic solutions for a 1D-model with nonlocal velocity via mass transport
Lucas C. F. Ferreira, Julio C. Valencia-Guevara
This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents si…