摘要：In 2011, Z. Lei and F. Lin presented a proof of existence of a global mild solution of the three-dimensional Navier-Stokes equations in scale-critical function spaces based on the Wiener algebra, for sufficiently small initial data in full space. In 2015, H. Bae modified the technique used by Lei and Lin to prove lower bounds on the radius of analyticity of the solution obtained. Recently, Ambrose, Lopes Filho and Nussenzveig Lopes adapted Bae's argument to periodic flows, which changes the radius estimate a little. The same authors have adapted these ideas to revisiting the 2004 existence result by M. Cannone and G. Karch in spaces of pseudo-measures, extending it to a larger space of initial data, and to the scalar Kuramoto-Sivashinsky equation, where we improve known existence results and obtain new estimates on the radius of analyticity of the solution, both in spaces based on pseudo-measures and on the Wiener algebra. The purpose of this talk is to survey these results and illustrate the technique involved.

嘉宾简介：Prof. Lopes got his PhD in Mathematics from the University of California, Berkeley (1990). He was Semester Program Visitor of ICERM, Brown University and was long-term participant of the Isaac Newton Institute, University of Cambridge, 2022. He was faculty at the State University of Campinas 1992-2012 and is currently a full professor at the Department of Applied Mathematics of IM-UFRJ. His research focuses on mathematical modeling of the motion of incompressible fluids, especially from the point of view of rigorous analysis, using modern techniques of partial differential equations and functional analysis in the analytical treatment of irregular or turbulent flows. He was Associate Editor for SIAM Journal on Mathematical Analysis and other prestigious journals. He was elected Vice-Chair of the SIAM Activity Group on Analysis of PDE for 2017-2018.