Approximation of Stochastic Partial Differential Equations and Turbulence in Fluids
| Author | : Christoph Gugg |
| Publisher | : |
| Total Pages | : 108 |
| Release | : 2001-01 |
| Genre | : |
| ISBN | : 9783896392633 |
Approximation Of Stochastic Partial Differential Equations And Turbulence In Fluids
Download Approximation Of Stochastic Partial Differential Equations And Turbulence In Fluids full books in PDF, epub, and Kindle. Read online free Approximation Of Stochastic Partial Differential Equations And Turbulence In Fluids ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Stochastic Partial Differential Equations in Fluid Mechanics
| Author | : Franco Flandoli |
| Publisher | : Springer Nature |
| Total Pages | : 206 |
| Release | : 2023-06-11 |
| Genre | : Mathematics |
| ISBN | : 9819903858 |
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.
Turbulence in Fluids
| Author | : Marcel Lesieur |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 435 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 9400905335 |
Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is the problem to be solved. Extremely schematically, two opposing points of view have been advocated during these last ten years: the first one is "statistical", and tries to model the evolution of averaged quantities of the flow. This com has followed the glorious trail of Taylor and Kolmogorov, munity, which believes in the phenomenology of cascades, and strongly disputes the possibility of any coherence or order associated to turbulence. On the other bank of the river stands the "coherence among chaos" community, which considers turbulence from a purely deterministic po int of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community are also associated the experimentalists who seek to identify coherent structures in shear flows.
Stochastic Partial Differential Equations: Six Perspectives
| Author | : René Carmona |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 349 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821821008 |
The field of Stochastic Partial Differential Equations (SPDEs) is one of the most dynamically developing areas of mathematics. It lies at the cross section of probability, partial differential equations, population biology, and mathematical physics. The field is especially attractive because of its interdisciplinary nature and the enormous richness of current and potential future applications. This volume is a collection of six important topics in SPDEs presented from the viewpoint of distinguished scientists working in the field and related areas. Emphasized are the genesis and applications of SPDEs as well as mathematical theory and numerical methods. .
Probabilistic Methods in Fluids
| Author | : Ian Malcolm Davies |
| Publisher | : World Scientific |
| Total Pages | : 383 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9812703985 |
This volume contains recent research papers presented at the international workshop on OC Probabilistic Methods in FluidsOCO held in Swansea. The central problems considered were turbulence and the NavierOCoStokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media."
Instabilities and Nonequilibrium Structures VI
| Author | : E. Tirapegui |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401142475 |
This book contains two introductory papers on important topics of nonlinear physics. The first one, by M. San Miguel et al., refers to the effect of noise in nonequilibrium systems. The second, by M.E. Brachet, is a modern introduction to turbulence in fluids. The material can be very useful for short courses and is presented accordingly. The authors have made their texts self-contained. The volume also contains a selection of the invited seminars given at the Sixth International Workshop on Instabilities and Nonequilibrium Structures. Audience: This book should be of interest to graduate students and scientists interested in the fascinating problems of nonlinear physics.
Stochastic Analysis and Partial Differential Equations
| Author | : Gui-Qiang Chen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 290 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821840592 |
This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.
New Trends and Results in Mathematical Description of Fluid Flows
| Author | : Miroslav Bulíček |
| Publisher | : Springer |
| Total Pages | : 190 |
| Release | : 2018-09-26 |
| Genre | : Mathematics |
| ISBN | : 331994343X |
The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.
Mathematical Foundation of Turbulent Viscous Flows
| Author | : P. Constantin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2006-01-10 |
| Genre | : Mathematics |
| ISBN | : 9783540285861 |
Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.
Turbulence in Fluid Flows
| Author | : George R. Sell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 208 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461243467 |
The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.
