Pedro Fernández D.
Assistant professor, Universidad de las Américas UDLA
I'm working on the Navier-Stokes equations: on the existence of explosive solutions and regularity.
Upcoming activities of interest
Articles
Micropolar fluids starting from initial angular velocities with negative Sobolev regularity, Preprint (2024)
Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity, Mathematische Annalen (2023) with Tobias Barker and Christophe Prange (arXiv:2302.06509)
Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl, Journal of Mathematical Fluid Mechanics (2021) with Pierre Gilles Lemarié-Rieusset (arXiv:2010.00868)
On the use of the Riesz Transforms to determine the pressure term in the incompressible Navier–Stokes equations on the whole space, Acta Applicandae Mathematicae (2021) with Borys Alvarez Samaniego and Wilson P. Alvarez Samaniego (arXiv:2004.02588)
Discretely self-similar solutions for 3D MHD equations and global weak solutions in weighted L2 spaces, Journal of Mathematical Fluid Mechanics (2021) with Oscar Jarrin (arXiv:1910.11267)
Weak-strong uniqueness in weighted L2 spaces and weak suitable solutions in local Morrey spaces for the MHD equations, Journal of Differential Equations (2021) with Oscar Jarrin (arXiv:2002.10531)
Characterisation of the pressure term in the incompressible Navier–Stokes equations on the whole space, Disc. Cont. Dyn. Systems DCDS (2020) with Pierre Gilles Lemarié-Rieusset (arXiv:2001.10436)
Weak solutions for Navier–Stokes equations with initial data in weighted L2 spaces, Arch Rational Mech Anal (2020), with Pierre Gilles Lemarié-Rieusset (arXiv:1906.11038)
Current interests
Discretely selfsimilar solutions
Results of epsilon-regularity for the Navier-Stokes equations
CV Link to pdf
Teaching activity
2023 Physics (Undergraduate, Universidad de las Américas, Ecuador)
2023 Exercices courses on analysis-probability (pré-ING 2, CY Tech, France)
2020 Exercices courses on analysis (Undergraduate, Université d'Evry, France)
2019 Exercices courses on analysis (Undergraduate, Université d'Evry, France)
Thesis
Mathematics, Study of the existence of infinite energy weak solutions to the incompressible Navier-Stokes equations
Advisor : Pierre Gilles Lemarié-Rieusset
Université Paris Saclay
Doctoral School of Mathematics Hadamard EDMH, Laboratoire de Mathématiques et Modélisation d’Évry LaMME (France).