One-dimensional turbulence and the stochastic Burgers equation /

One-dimensional turbulence and the stochastic Burgers equation /

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Bibliographic Details
Author / Creator:	Boritchev, Alexandre, 1986- author.
Imprint:	Providence, Rhode Island : American Mathematical Society, [2021] ©2021
Description:	vii, 192 pages : illustrations ; 26 cm.
Language:	English
Series:	Mathematical surveys and monographs, 0076-5376 ; volume 255 Mathematical surveys and monographs ; no. 255.
Subject:	Stochastic partial differential equations. Burgers equation. Turbulence -- Mathematical models. Burgers equation. Stochastic partial differential equations. Turbulence -- Mathematical models.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12634191

Hidden Bibliographic Details
Other authors / contributors:	Kuksin, Sergej B., 1955- author.
ISBN:	9781470464363 1470464365 9781470465643
Notes:	Includes bibliographical references (pages 183-190) and index.
Summary:	This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3-law, and the Kolmogorov-Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L₁-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.

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Call Number:	QA274.25.B67 2021 c.1
c.1	Available Loan period: standard loan Scan and Deliver Request for Pickup Need help? - Ask a Librarian