Hi, my name is

David Llerena.

CV

About Me

I defended my Ph.D. in December 2024 at the Laboratoire de Mathématiques et Modélisation d’Évry (LaMME). My doctoral research was conducted under the supervision of Diego Chamorro and Pierre-Gilles Lemarié-Rieusset.

My research interests focus on the local regularity theory of weak solutions for models derived from fundamental fluid mechanics, including the Navier-Stokes equations, MHD equations, and micropolar equations

    Education

    2021 - 2024
    Ph.D in Mathematics
    Université Paris-Saclay, Laboratoire de Mathématiques et Modélisation d'Évry

    Thesis title: On the interdependence of variables in the study of some equations in fluid mechanics.

    Advisors: Diego Chamorro and Pierre-Gilles Lemarié-Rieusset.

    2023 - 2024
    Master degree in Mathematics
    Université Paris Saclay site Orsay

    M2 Analyse, Arithmétique, Géométrie

    Master thesis: Étude de la régularité pour quelques équations de la mécanique des fluides.

    Rapport
    BS.c. in Applied Mathematics
    Universidad Central del Ecuador

    Thesis: Aproximate identities in the Schwarzs spaces.

    Advisor: Borys Alvarez-Samaniego

    Research

    1. Partial regularity and L3-norm concentration effects around possible blow-up points for the micropolar fluid equations.
    Preprint, 2024
    Joint work with: Diego Chamorro
    preprint
    2. Partial suitable solutions for the micropolar equations and regularity properties.
    Accepted in: Annales Mathématiques Blaise Pascal, 2024
    Joint work with Diego Chamorro
    preprint
    3. Some remarks about the stationary Micropolar fluid equations: existence, regularity and uniqueness
    Journal of Mathematical Analysis and Applications, 2024
    Joint work with Diego Chamorro and Gaston Vergara-Hermosilla
    preprint , Journal
    4. A crypto-regularity result for the micropolar fluids equations
    Journal of Mathematical Analysis and Applications, 2022
    Joint work with Diego Chamorro
    preprint , Journal
    5. Interior ϵ-regularity theory for the solutions of the magneto-micropolar equations with a perturbation
    Journal of Elliptic and Parabolic Equations, 2022
    Joint work with Diego Chamorro
    preprint , Journal
    6. Approximate identities for the Schwartz space
    Analysis and Mathematical Physics , 2021
    Joint work with Boris Alvarez-Samaniego and Wilson Alvarez-Samaniego
    Journal

    Conferences

    Given talks, posters and seminars

    2024:
    • IV Conferencia internacional en análisis y ecuaciones diferenciales parciales, Julio, Quito-Ecuador
    • X Conferencia de Matemáticos Ecuatorianos en París (Con-MateP), April, Paris-France
    2023:
    • XI Conferencia de matemáticos ecuatorianos en Paris, November, Paris-France
    • Vulgarization seminar for master students M1 MEEF from Université Paris-Saclay, October, Evry-France.
    • Poster session at "New trends in mathematical fluids dynamics", June, Grenoble-France, poster
    • Séminaire des doctorants en EDP, LMO, Orsay-France.
    • Séminaire des doctorants, LaMME, Evry-France.
    • Poster session at "Journées de jeunes EDPistes", Tours-France.
    2022:
    • IV Jornadas Ecuatorianas de Matemática, November, Quito-Ecuador
    • II Conferencia internacional en analisis y ecuaciones en derivadas parciales, April, Quito- Ecuador

    Attended conferences and worshops

    2023:
    • New trends in mathematical fluids dynamics, June, Grenoble.
    2022:
    • Mathflows, Marseille Luminy, December.
    • VIII Conferencia de Matemáticos Ecuatorianos en París, September, Paris.
    • Summer school on fluids and turbulence, Lyon, June.
    • Mathematical Advances in Geophysical Flows, April, Marseille Luminy.
    • GDR EDP Conférence itinérante, February, Vannes.
    2021:
    • VII Conferencia de Matemáticos Ecuatorianos en París, October, Paris.
    • Les Journées du GDR AFHP 2021, Besançon, September.

    Teaching

    As a tutor at Universite d'Evry:
    • Sept 2022 - April 2024:
      1. "Langage Mathématique" for 1st year undergraduates in mathematics, Université d'Evry.
      2. Mathematical techniques for 2nd year undergraduates in chemistry (Linear algebra and multivariable calculus) , Université d'Evry.
    • Oct 2021 - April 2022:
      1. Mathematical techniques for 2nd year undergraduates in economy, Université d'Evry.
      2. Langage Mathématique for 1st year undergraduates in mathematics, Université d'Evry.
      3. Mathematical techniques for 2nd year undergraduates in chemistry (Linear algebra and multivariable calculus), Université d'Evry.
      4. Mathematical techniques for 2nd year undergraduates in physics (Convergence of sequences and series), Université d'Evry.
    Summer School (In spanish):
    In Sept 2023 I gave a mini-course (online) on the local regularity of the Navier-Stokes equations for for the Summer school in analysis, AMARUN
    1. Lecture 1
    2. Lecture 2
    3. Lecture 3
    4. Lecture 4

    You can reach me at my mail david.llerena@univ-evry.fr