Singularities in Fluids and General Relativity

Overview

Singularity formation arises in many fundamental equations in fluid dynamics and general relativity, such as black hole formation in general relativity, shock formation and implosion in compressible fluid equations, self-similar blow-up in incompressible fluid equations. While the mechanisms for these singularity formations are different, some of the mathematical ideas are linked to each other, and cross-fertilization in these different equations could lead to further non-incremental progress in the field. This program aims to bring experts on singularity formation that come from different areas of PDE and mathematical physics together, to exchange ideas and techniques along the following themes:

• Singularity in incompressible fluids: interplay between analysis and numerics
• Self-similarity and implosion, with or without gravity
• Nonlinear wave equations and its connection to shock formation
• Formation and stability of black holes
• Emergence and instability of naked singularities

We expect that the combined effort of the participants with complementary strength will generate new ideas and innovative strategies in fluid dynamics and general relativity, as well as inspire junior researchers participating in the program.