Singularities and Asymptotic Patterns in Fluids and Evolutionary PDEs (25w5330)

The Institute of Mathematics at the University of Granada will host the "Singularities and Asymptotic Patterns in Fluids and Evolutionary PDEs" workshop at the University of Granada (IMAG) in Spain, from May 11 - 16, 2025.

Mathematical models for natural phenomena are typically expressed as evolutionary nonlinear partial differential equations (PDEs). Of particular interest is the analysis of asymptotic patterns or singular limits. This pertains to the existence of regions with high concentration for the quantity represented by the solution of a given PDE. Such concentration can be triggered by either an explicit or hidden parameter within the model, which approaches a critical limiting value, or by the progression of time towards infinity, or an instance when a form of blow-up occurs. In recent years, significant advancements have been made in this field, particularly concerning PDEs in fluids, geometric analysis, and reaction-diffusion equations. The purpose of this workshop is to showcase some of these recent developments and examine technical similarities across these subfields. More precisely, the following topics will be discussed at the workshop:

- Singularity and small-scale formations in incompressible fluids
- Implosion and shock in compressible fluids
- Singularity formation in geometric flows
- Singularity formation and asymptotic patterns in chemotaxis
- Long-time asymptotics of evolutionary PDEs

The Institute of Mathematics at the University of Granada(IMAG) in Granada, Spain, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta Technology and Innovation.