N. N

Prof. Dr. Sebastian Herr (Universität Bielefeld): Global wellposedness of the Zakharov System below the ground state, Kolloquium Partial Differential Equations

Tuesday, 25.10.2022 14:15 im Raum M5

Mathematik und Informatik

The Zakharov system is a quadratically coupled system of a Schrödinger and a wave equation, which is related to the focussing 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.

Angelegt am 18.10.2022 von N. N
Geändert am 23.01.2023 von N. N
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