One-dimensional turbulence and the stochastic Burgers equation /

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 e...

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Bibliographic Details
Main Authors: Boritchev, Alexandre, 1986- (Author), Kuksin, Sergej B., 1955- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2021]
Series:Mathematical surveys and monographs ; no. 255.
Subjects:

MARC

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245 1 0 |a One-dimensional turbulence and the stochastic Burgers equation /  |c Alexandre Boritchev, Sergei Kuksin. 
264 1 |a Providence, Rhode Island :  |b American Mathematical Society,  |c [2021] 
264 4 |c ©2021 
300 |a vii, 192 pages :  |b illustrations ;  |c 26 cm. 
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490 1 |a Mathematical surveys and monographs ;  |v volume 255 
504 |a Includes bibliographical references and index. 
505 0 |a Basic results -- Asymptotically sharp estimates for Sobolev norms of solutions -- Mixing in the stochastic Burgers equation -- Stochastic Burgers equation in the space L₁ -- Notes and comments, I -- Turbulence and burgulence -- Rigorous burgulence -- The inviscid limit and inviscid burgulence -- Notes and comments, II -- Miscellanea -- Appendices -- Solutions for selected exercises. 
520 |a 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 generalized 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. 
650 0 |a Stochastic partial differential equations.  |0 http://id.loc.gov/authorities/subjects/sh87001697 
650 0 |a Burgers equation.  |0 http://id.loc.gov/authorities/subjects/sh85018060 
650 0 |a Turbulence  |x Mathematical models.  |0 http://id.loc.gov/authorities/subjects/sh2008113041 
700 1 |a Kuksin, Sergej B.,  |d 1955-  |e author.  |0 http://id.loc.gov/authorities/names/n93089555 
830 0 |a Mathematical surveys and monographs ;  |v no. 255.  |0 http://id.loc.gov/authorities/names/n83732928 
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