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Global well-posedness of the Zakharov System below the ground state

发布时间:2022-11-23 浏览量:67

时   间:  2022-11-23 16:00 — 17:00

地   点:  Zoom APP(2)()
报告人:  Sebastian Herr
单   位:  Bielefeld University
邀请人:  张登
备   注:  Zoom会议: 686-3535-9310(密码:280293).报告人介绍:Sebastian Herr,德国比勒费尔德大学教授(W3),主要从事偏微分方程,尤其是色散方程的研究。在 Duke Math. J., JEMS, Amer. J. Math, Adv. Math., ARMA, CMP 等国际权威期刊发表多篇论文。
报告摘要:  

The Zakharov system is a quadratically coupled system of a Schrödinger and a wave equation, which is related to the focusing 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 bi-linear Fourier extension estimate. This is joint work with Timothy Candy and Kenji Nakanishi.