| 29.01.2015 | André Hänel (Universität Stuttgart) |
| 13.00 Uhr | Eigenvalue asymptotics for the Laplacian on an infinite strip with mixed boundary condition |
| 22.01.2015 | Jean-Marie Barbaroux (Université de Toulon) |
| | Absolute continuity of the spectrum for a model of weak decay of  boson |
| | Abstract: We study spectral properties of a Hamiltonian describing the weak decay of a boson into a pair of electron and positron. The operator acts on tensor product of one bosonic and two fermionic Fock spaces. Our main result states that the nature of the spectrum near thresholds is purely absolutely continous. As usual for energies near thresholds, the derivation of positive commutator estimates fails with "standard" conjugate operators. Therefore, to derive a Mourre inequality, we follow the strategy of Huebner and Spohn they use for the spectral study of a spin-boson model, and we apply singular Mourre theory with a non self-adjoint conjugate operator. This is joint work with Jeremy Faupin and Jean-Claude Guillot. |
| 15.01.2015 | Vu Hoang (Rice University, Texas) |
| | Blowup for model equations of fluid mechanics. |
| | Abstract: The 3D Euler equations describe the motion of an inviscid, incompressible fluid. One of the most challenging questions is whether the solutions of the Euler equations develop singularities in finite time from smooth initial data. In 2013, remarkable progress has been made in the understanding of possible singularity formation for inviscid fluids. In particular, striking numerical evidence has been found by T. Hou and G. Luo that indeed blowup solutions exist for the 3D Euler equations. Inspired by this, A. Kiselev and V. Sverak found solutions of the 2D Euler equations with double exponential gradient growth in time. In this talk, I give an introduction into recent developments and discuss one-dimensional model problems. |
