An Introduction to the Mathematics of Hydrodynamic Stability at High Reynolds Number
Jacob Bedrossian
University of California, Los Angeles, USA
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The mathematical theory of hydrodynamic stability has undergone remarkable developments in recent decades, revealing subtle mechanisms of stability and instability that required new mathematical ideas to capture, even for the simplest stationary solutions of the incompressible Euler and Navier–Stokes equations.
This book introduces the fundamental mathematical ideas behind some of these developments, from classical spectral stability theory to more recent advances in inviscid damping, enhanced dissipation, and nonlinear stability. Particular emphasis is placed on understanding the physical mechanisms at work and the mathematical methods used to study them.
The book combines detailed proofs of selected results with broader summaries and discussions of some of the modern theoretical advances, aiming to give graduate students and researchers the background and wide perspective needed to engage with this rapidly developing subject.