Online Analysis and PDE seminar

  • Biweekly seminar series, bringing together those within the field of Analysis and PDEs to present their work.

  • Runs 15:00-16:00 on Wednesdays, hosted by the ICMAT using ZOOM.

  • Organized by:
    Universidad Autónoma de Madrid (UAM)
    Universidad de Cantabria (UC)
    Universidad Carlos III (UC3M)
    Universidad Complutense de Madrid (UCM)
    Instituto de Ciencias Matemáticas (ICMAT)
    Instituto de Matemáticas de la Universidad de Sevilla (IMUS)

  • To attend the seminar:
    1) ZOOM will be used. You will not need a license.

2) Link to the seminar:

You can write to onlineapdeseminar(at) to join the mailing list and receive and an announcement of each seminar.



Maria Colombo, EPFL


Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations.

Abstract: In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk we exhibit two distinct Leray solutions with zero initial velocity and identical body force.

The starting point of our construction is Vishik's answer to another long-standing problem in fluid dynamics, namely whether the Yudovich uniqueness result for the 2D Euler system can be extended to the class of $L^p$-integrable vorticity. Building on Vishik's work, we construct a `background' solution which is unstable for the 3D Navier-Stokes dynamics in similarity variables; the second solution from the same initial datum is a trajectory on the unstable manifold associated to the background solution, in accordance with the predictions of Jia and Sverak.



The seminar will resume in October