Intermittent Convex Integration for the 3D Euler Equations: (AMS-217)

Tristan Buckmaster

ISBN 10: 0691249555 / ISBN 13: 9780691249551

Editore: Princeton University Press, 2023

New copy - Usually dispatched within 4 working days. Codice articolo B9780691249551

Riassunto:

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.

Informazioni sull'autore: 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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Titolo: Intermittent Convex Integration for the 3D ...
Casa editrice: Princeton University Press
Data di pubblicazione: 2023
Legatura: Hardback
Condizione: New