We intend to get acquainted with the most important results on instability mechanisms for incompressible Euler equations, which are currently the best hope for showing the sharpest blowup and non-uniqueness results, both for Euler and for Navier-Stokes equations.
The tentative plan is
- Recalling classical existence results for Euler equations.
- Small scale creation and optimal growth bounds in two dimensions (along Kiselev-Sverak).
- Low-rank approximation of Biot-Savart and blowups for $C^{1,\alpha}$ data in three dimensions (along Elgindi).
- Non-uniqueness for forced Euler and Navier-Stokes in three dimensions via spectral instability (along how people understand and develop ideas of Vishik)
The seminar will be held on Wednesdays at 13:15 and starts on 20.04.2021. Anyone interested is welcome to contact us at burczak@math.uni-leipzig.de or gebhard@math.uni-leipzig.de
Jan Burczak&Bjorn Gebhard
- Trainer/in: Jan Burczak