Webrelaunch 2020

Global wellposedness of the Zakharov System below the ground state

  • Speaker: Prof. Dr. Sebastian Herr
  • Place: SR 1.067 and via Zoom
  • Time: 9.2.2023, 14:00 - 9.2.2023, 15:00


The Zakharov system is a quadratically coupled system of a Schrödinger and a wave equation, which is related to the focusing cubic Schrödinger equation. We consider the associated Cauchy problem in the energy-critical dimension d=4 and prove that it is globally well-posed in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold.
The result is based on a uniform Strichartz estimate for the Schrödinger equation with potentials solving the wave equation. A key ingredient in the non-radial setting is a bilinear Fourier extension estimate. This is joint work with Timothy Candy and Kenji Nakanishi.