Stochastic partial differential equations in fluid mechanics / Franco Flandoli, Eliseo Luongo.
Flandoli, Franco, author.; Luongo, Eliseo, author.
2023
QA901
Available Online

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Title Stochastic partial differential equations in fluid mechanics / Franco Flandoli, Eliseo Luongo.
Author Flandoli, Franco, author.
ISBN 9789819903856 (electronic bk.)
9819903858 (electronic bk.)
9789819903849
981990384X
DOI https://doi.org/10.1007/978-981-99-0385-6
Published Singapore : Springer, [2023]
Copyright ©2023
Language English
Description 1 online resource (viii, 199 pages).
Item Number 10.1007/978-981-99-0385-6 doi
Call Number QA901
Dewey Decimal Classification 532
Summary This book is devoted to stochastic Navier–Stokes equations and more generally to stochasticity in fluid mechanics. The two opening chapters describe basic material about the existence and uniqueness of solutions: first in the case of additive noise treated pathwise and then in the case of state-dependent noise. The main mathematical techniques of these two chapters are known and given in detail for using the book as a reference for advanced courses. By contrast, the third and fourth chapters describe new material that has been developed in very recent years or in works now in preparation. The new material deals with transport-type noise, its origin, and its consequences on dissipation and well-posedness properties. Finally, the last chapter is devoted to the physical intuition behind the stochastic modeling presented in the book, giving great attention to the question of the origin of noise in connection with small-scale turbulence, its mathematical form, and its consequences on large-scale properties of a fluid.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 14, 2023).
Added Author Luongo, Eliseo, author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2330. 1617-9692
Available in Other Form Print version: 9789819903849
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Chapter
1 The Navier–Stokes Equations with Deterministic Rough Force, Chapter
2 Stochastic Navier–Stokes Equations and State–Dependent Noise, Chapter
3 Transport Noise in the Heat Equation, Chapter
4 Transport Noise in the Navier–Stokes Equations, Chapter
5 From Small–Scale Turbulence to Eddy Viscosity and Dissipation.

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