Colóquio de Matemática

10/04/2026, 14h - Auditório Airton Silva

Prof.a Dr.a Gabriela Planas 

Universidade Estadual de Campinas (Unicamp)

Título: The Fate of Nonlinear Flows: Decay in Critical Spaces

Resumo: What ultimately happens to nonlinear flows as time evolves? Do they persist, or do they gradually fade away? Understanding how fast solutions decay is key to explaining how complex systems dissipate energy while still reflecting the influence of the initial data.

In this talk, we explore decay rates for a class of nonlinear dissipative equations, including the Navier–Stokes equations and related models. Our focus is on solutions in critical Sobolev spaces, where the natural scaling of the equations makes the analysis particularly delicate.

We show that the long-time behavior of solutions is determined by properties of the initial data, leading to precise algebraic decay rates. This perspective also reveals the distinct roles played by linear dissipation and nonlinear effects.

A central feature of this analysis is that it is carried out entirely within the critical framework, providing a new approach to obtaining decay estimates for nonlinear equations.