Intermittent Convex Integration for the 3D Euler Equations

AMS-217

Tristan Buckmaster, Nader Masmoudi, Matthew Novack , Vlad Vicol

$135

Paperback

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English

Princeton University Press
18 October 2023

Geometry

Series: Annals of Mathematics Studies

A new threshold for the existence of weak solutions to the incompressible Euler equations

To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.

By: Tristan Buckmaster, Nader Masmoudi, Matthew Novack, Vlad Vicol
Imprint: Princeton University Press
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691249544
ISBN 10: 0691249547
Series: Annals of Mathematics Studies
Pages: 256
Publication Date: 18 October 2023
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

Tristan Buckmaster is professor of mathematics at the University of Maryland. Nader Masmoudi is professor of mathematics at New York University. Matthew Novack is assistant professor of mathematics at Purdue University. Vlad Vicol is professor of mathematics at New York University.

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Intermittent Convex Integration for the 3D Euler Equations

AMS-217

Tristan Buckmaster, Nader Masmoudi, Matthew Novack , Vlad Vicol

$135

Paperback

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