Stochastic Partial Differential Equations in Fluid Mechanics / Franco Flandoli and Eliseo Luongo.
 Format
 Book
 Language
 English
 Εdition
 First edition.
 Published/Created

 Singapore : Springer, [2023]
 ©2023
 Description
 1 online resource (206 pages)
Details
 Subject(s)
 Series

 Lecture notes in mathematics & computer science ; Volume 2330. [More in this series]
 Lecture Notes in Mathematics Series ; Volume 2330
 Summary note
 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 statedependent 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 transporttype noise, its origin, and its consequences on dissipation and wellposedness 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 smallscale turbulence, its mathematical form, and its consequences on largescale properties of a fluid.
 Bibliographic references
 Includes bibliographical references.
 Source of description
 Description based on print version record.
 Contents

 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.
 ISBN
 9819903858
 Doi
 10.1007/9789819903856
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