应兰州大学数学与统计学院邀请，Bergen大学的DidierPilod副教授将于2021年5月26日在线举办专题学术报告。

报告题目:Global well-posedness and scattering for theDysthe equation in L^2(R^2)

报告摘要：The Dysthe equation is a higher order approximation of the water waves system in the modulation (Schrodinger) regime and in the infinite depth case. After reviewing the derivation of the Dysthe and related equations, we will focus on the initial-value problem.

We prove a small data global well-posedness and scattering result in the critical space L^2(R^2). This result is sharp in view of the fact that the flow map cannot be C^3 continuous below L^2(R^2). Our analysis relies on linear and bilinear Strichartz estimates in the context of the Fourier restriction norm method. Moreover, since we are at a critical level, we need to work in the framework of the atomic space U_S^2 and its dual V_S^2 of square bounded variation functions. We also prove that the initial-value problem is locally well-posed in H^s(R^2), s > 0. Our results extend to the finite depth version of the Dysthe equation. This talk is based on a joint work with Razvan Mosincat (University of Bergen) and Jean-Claude Saut (Universite Paris-Saclay).

时 间：5月26日（星期三）16：00

地 点：理工楼518 （Zoom Meeting）

自行参与：ZoomMeeting ID: 657 4001 8157 Password: W9uzaNSU

Didier Pilod副教授简介

Didier Pilod，Bergen大学副教授, 博士毕业于巴西纯粹与应用数学研究所，导师为国际著名色散偏微分方程专家F.Linares，之后跟随国际数学联盟主席C.E.Kenig从事博士后研究工作。Didier Pilod的工作在色散偏微分方程领域有重要影响，他目前已在“Math. Ann.”、“Comm. Math. Phys.”、“Arch. Ration. Mech. Anal.”、“Anal. PDE”、“Trans. Amer. Math. Soc.”、“Ann. Inst. H. Poincare Anal. Non Lineaire”、“Comm. Partial Differential Equations”、“Rev. Mat. Iberoam.”、“SIAM J. Math. Anal.”等国际重要学术期刊上发表论文多篇。

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2021年5月24日