报告地点：行健楼学术活动室665

邀请人：寿凌云

摘要：This talk discusses linear and nonlinear estimates for quasilinear parabolic systems with Neumann boundary conditions on bounded domains. The main focus is the construction of a critical Besov framework starting from the Sobolev realization of the Neumann Laplacian on the mean-free space. We explain how analytic semigroup theory, sectorial operators, the Da Prato--Grisvard theorem, and Amann’s interpolation results combine to yield maximal regularity estimates in critical Besov spaces.

These linear estimates are then applied to separated divergence-form systems near a constant equilibrium. The nonlinear terms are treated perturbatively, leading to a small-data global a priori estimate. We also discuss the limitations of this approach, in particular the distinction between constant-coefficient estimates and genuine variable-coefficient local theory, as well as the additional difficulties caused by general conormal boundary conditions.

报告人简介：

Qimeng Zhu is a PhD student at LAMA, Université Paris-Est Créteil, under the supervision of Raphaël Danchin. His PhD is funded by a CDSN doctoral fellowship from ENS-PSL.

His research interests include quasilinear parabolic systems, critical Besov spaces, analytic semigroups, maximal regularity, and hyperbolic systems with partial dissipation.