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Forschungsseminar (Dauerveranstaltung)

Vorträge im Sommersemester 2022

Die Vorträge finden in Präsenz im Seminarraum 2.066 im Mathematikgebäude 20.30 statt.

03.05.2022, 14:00 Uhr Peer Christian Kunstmann (Karlsruhe)

Functional calculi for Stokes operators with first order boundary conditions on unbounded domains
We study functional calculi in L^q for Stokes operators with Hodge, Navier, and Robin type boundary conditions on uniform C^{2,1}-domains \Omega\subseteq\R^d. Our research complements recent results on the L^q-theory of such operators and also sheds new light on the cases q=1 and q=\infty.

17.05.2022, 14:00 Uhr 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 L^p estimates we require a more refined wave packet analysis.

24.05.2022, 14:00 Uhr 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, 14:00 Uhr 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, 14:00 Uhr 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 \mathbb{R}^4 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, 14:00 Uhr Richard Nutt (Karlsruhe)

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