This book originated from a 1988 summer school on mathematical physics, inspired by the late Marvin Shinbrot's vision for a comprehensive work on the Boltzmann equation. Despite initial ambitions, the authors adapted their approach to compile significant, often scattered results from the last two decades, aiming for clarity and rigor.
Incompressible nonviscous flows, a key area in fluid dynamics, revolve around the Euler equation, which describes the velocity field of fluids. Despite being established in 1755, significant questions about the equation's solutions remain unresolved, particularly regarding singularities and the long-term behavior of smooth solutions. This ongoing complexity has attracted the attention of many mathematicians, making the study of perfect flows a vibrant and challenging segment of applied mathematics, rich with diverse mathematical techniques and theories.