One-dimensional turbulence and the stochastic Burgers equation
- Responsibility
- Alexandre Boritchev, Sergei Kuksin
- Publication
- Providence, Rhode Island : American Mathematical Society, [2021]
- Copyright notice
- ©2021
- Physical description
- vii, 192 pages : illustrations ; 26 cm
- Series
- Mathematical surveys and monographs ; no. 255.
At the library
Science Library (Li and Ma)
Stacks
| Call number | Status |
|---|---|
| QA3 .A4 V.255 |
More options
Description
Creators/Contributors
- Author/Creator
- Boritchev, Alexandre, 1986- author.
- Contributor
- Kuksin, Sergej B., 1955- author.
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 183-190) and index
- Contents
-
- Introduction Stochastic Burgers equation: Basic results Asymptotically sharp estimates for Sobolev norms of solutions Mixing in the stochastic Burgers equation Stochastic Burgers equation in the space $L_1$ Notes and comments, I One-dimensional turbulence: Turbulence and burgulence Rigorous burgulence The inviscid limit and inviscid burgulence Notes and comments, II Additional material: Miscellanea Appendices Solutions for selected exercises Acknowledgements Bibliography Index.
- (source: Nielsen Book Data)
- 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 $L_1$-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.
(source: Nielsen Book Data)
Subjects
- Subjects
- Stochastic partial differential equations.
- Burgers equation.
- Turbulence > Mathematical models.
- Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} -- Stochastic analysis [See also 58J65] -- Stochastic partial differentia.
- Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Conservation laws.
- Partial differential equations -- Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] -- PDEs in connection with fluid mechanics.
- Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Ergodic theory [See also 28Dxx] -- Ergodicity, mixing, rates of mixing.
- Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Turbulence [See also 37-XX, 60Gxx, 60Jxx] -- Fundamentals.
- Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Turbulence [See also 37-XX, 60Gxx, 60Jxx] -- Turbulent transport, mixing.
Bibliographic information
- Publication date
- 2021
- Copyright date
- 2021
- Series
- Mathematical surveys and monographs, 0076-5376 ; volume 255
- ISBN
- 9781470464363 paperback
- 1470464365 paperback
- 9781470465643 electronic book
Browse related items
Start at call number:
