Main subject categories: • Stationary partial differential equations • Differential equations • Partial differential equations • Evolutionary Partial differential equations • Euler Equations and Related Hyperbolic Conservation Laws • Blow-up of Solutions of Supercritical Parabolic Equations • The Boltzmann Equation and Its Hydrodynamic Limits • Long-Time Behavior of Solutions to Hyperbolic Equations with Hysteresis • Mathematical Issues Concerning the Navier–Stokes Equations and Some of Its Generalizations • Evolution of Rate-Independent Systems • On the Global Weak Solutions to a Variational Wave EquationThis is the second volume in the seriesEvolutionary Equations, part of theHandbook of Differential Equationsproject. Whereas Volume I was intended to provide an overview of diverse abstract approaches, the guiding philosophy of the present volume is to offer a representative sample of the most challenging specific equations and systems arising in scientific applications.Three chapters are devoted to the modern mathematical theory of fluid dynamics: Chapter 1 deals with the Euler equations, Chapter 5 provides a general introduction to the theory of incompressible viscous fluids, and Chapter 3 discusses the asymptotic limits of discrete mechanical systems described by the Boltzmann equation.In a different direction, Chapter 2 introduces the blow-up phenomena of solutions of general parabolic equations and systems.Chapters 4 and 6 are closely related and deal with mathematical problems arising in materials science.Finally, Chapter 7 explores the topic of nonlinear wave equations.