### Research Seminar (Continuing Class)

Talks in summer 2022 |
---|

The talks are taking place in presence in seminar room 2.066.

03.05.2022, 2:00 pm | Peer Christian Kunstmann (Karlsruhe) |

*Functional calculi for Stokes operators with first order boundary conditions on unbounded domains*

We study functional calculi in for Stokes operators with Hodge, Navier, and Robin type boundary conditions on uniform -domains . Our research complements recent results on the -theory of such operators and also sheds new light on the cases and .

17.05.2022, 2:00 pm | Dorothee Frey (Karlsruhe) |

*Strichartz and dispersive estimates for equations with structured Lipschitz coefficients*

We shall discuss Strichartz estimates for both Schrödinger and wave equations with structured Lipschitz coefficients. The arguments are based on Phillips calculus, which allows to deduce dispersive estimates from the constant coefficient case. For fixed time estimates we require a more refined wave packet analysis.

24.05.2022, 2:00 pm | Christopher Bresch (Karlsruhe) |

*Local wellposedness of Maxwell systems with scalar-type retarded material laws*

In the first part of the talk, local wellposedness of an abstract retarded evolution equation is studied using the concept of a mild solution and Banach's fixed point theorem. The second part is an application to Maxwell equations in the context of a model from nonlinear optics.

31.05.2022, 2:00 pm | Robert Schippa (Karlsruhe) |

*Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions*

We consider Maxwell equations on a domain with perfectly conducting boundary conditions in isotropic media. In the charge-free case we recover Strichartz estimates due to Blair-Smith-Sogge for wave equations on domains. We shall also consider the quasilinear case of the Kerr nonlinearity, in which case we recover the Strichartz estimates and well-posedness results from Euclidean space. This is joint work with Nicolas Burq (Universite Paris-Sud).

14.06.2022, 2:00 pm | Martin Spitz (Bielefeld) |

*Almost sure scattering for the energy-critical cubic nonlinear Schrödinger equation with supercritical data*

The local and global wellposedness theory of nonlinear dispersive equations with randomized data has attracted a lot of interest over the last years. In particular in the scaling-supercritical regime, where a deterministic wellposedness theory fails, randomization has become an important tool to study the generic behaviour of solutions.

In this talk we study the energy-critical NLS on with supercritical initial data. We present a randomization based on a unit-scale decomposition in frequency space, a decomposition in the angular variable, and a unit-scale decomposition in physical space. We then discuss the resulting (almost surely) improved space-time estimates for solutions of the linear Schrödinger equation with randomized data and how these estimates yield almost sure scattering for the energy-critical cubic NLS.

12.07.2022, 2:00 pm | Richard Nutt (Karlsruhe) |

*Exponential Decay of the quasilinear Maxwell system due to surface conductivity*

We consider a quasilinear Maxwell system on a bounded domain with absorbing boundary conditions and derive an estimate for the normal traces of the electric and magnetic field. This allows us to strengthen a result on exponential decay for small initial data.

25.07.2022 | TULKKA in Ulm |

11:30-12:15 | Robert Schippa (Karlsruhe) | Quasilinear and time-harmonic Maxwell equations |

12:15-13:45 | Lunch break | |

13:45-14:30 | David Ploß (Konstanz) | The Bi-Laplacian with Wentzell boundary conditions on Lipschitz Domains |

14:40-15:25 | Dennis Gallenmüller (Ulm) | Measure-valued low Mach limits |

15:25-16:10 | Coffee break | |

16:10-16:55 | Angkana Rüland (Heidelberg) | On Rigidity, Flexibility and Scaling Laws: The Tartar Square |

ab 17:45 | Dinner in the city centre of Ulm | |

Detailed information on TULKKA is available hier. |

26.07.2022, 2:00 pm | Maximilian Ruff (Karlsruhe) |

*A Fourier Integrator for the cubic Schrödinger equation at regularity*

In this talk I will present the topic of my master thesis which is based on a paper by Ostermann, Rousset and Schratz. They introduced a new exponential-type time integration method for the cubic Schrödinger equation. While only assuming regularity of the solution, -Convergence with order strictly larger than 1/2 was shown. An important ingredient in this context are discrete-time Strichartz estimates.

You can find previous talks in the archive of the research seminar.