Event Details

  • 📅 jueves 11 de diciembre -- 13:00
  • 📍 Aula A25, Facultad de Ciencias
  • 👤Conferenciante: Javier Peñafiel (ICMAT)
  • 📖 Título: Topology of weak solutions in fluid mechanics
  • 📄 Resumen: In this talk we will explore the role of topology in low-regularity fields describing fluids and plasmas. First, I will show that, unlike classical solutions, weak solutions of the steady Euler equations can have any prescribed topology. This is achieved by means of a novel convex integration scheme that preserves the topology of the field throughout the process. As an application, this provides counterexamples in a weak sense to Grad's conjecture on the axisymmetry of certain plasma equilibria. In the second part of the talk, I will discuss the construction of dissipative solutions of ideal MHD with nonzero helicity. Using a new approach that better respects the topology of the equations, we provide the first example of Hölder continuous solutions in which one quantity is dissipated while another is conserved, even in the absence of symmetry.