New Perspectives and Challenges in the Mathematical Treatment of Fluid Mechanics

Euler’s equations for fluid mechanics—introduced by Leonhard Euler in the 1750s—are among the first significant systems of Partial Differential Equations (PDEs) ever written. Yet, the behavior of solutions to these models remains surprisingly challenging at the mathematical level. In this talk, we will survey both longstanding and emerging questions, alongside recent perspectives on classical fluid models—both incompressible and compressible.