Giovanni Galdi Bücher

Focusing on boundary-value problems related to the Navier-Stokes equations, this comprehensive book explores existence, uniqueness, and regularity of solutions in both bounded and unbounded domains, including their asymptotic behavior. The latest edition merges two previous volumes and adds chapters on steady flow in exterior domains. Each chapter features preliminary discussions, alternative approaches, and historical notes, alongside over 400 exercises for students and researchers. A vast bibliography supports further exploration of the topics.

Focusing on Nonlinear Stationary Problems, this volume delves into the Navier-Stokes equations, exploring essential mathematical properties like existence, regularity, and uniqueness of solutions. It addresses various motion scenarios in bounded and unbounded domains, highlighting ongoing challenges and presenting conjectures for unresolved issues. The text is self-contained and accessible, featuring over 200 exercises, chapter summaries, and questions, making it an ideal resource for theoretical Fluid Mechanics courses and self-study, while also serving as a valuable reference.

The content of the volume is constituted by four articles. The first concerns the theory of propagation of plane waves in elastic media. The second treats theoretically the linear, weakly non-linear, and non-linear stability of flows of a viscous incompressible fluid in a diverging channel. The third lecture investigates the mathematical properties of the equations governing the motion of a viscous incompressible second-grade fluid, such as existence, uniqueness of classical solutions and stability of steady-state flows. The last lecture provides some basic results on wave propagation in continuum models. The objective of this book is to emphasize and to compare the various aspects of interest which include the necessary mathematical background, constitutive theories for material of differential type, polarized and shock waves, and second sound in solids at low temperatures.