Franco Flandoli's Books

Random Perturbation of PDEs and Fluid Dynamic Models

École D’Été de Probabilités de Saint-Flour XL – 2010

By: Franco Flandoli

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Random Perturbation of PDEs and Fluid Dynamic Models

École D’Été de Probabilités de Saint-Flour XL – 2010

By: Franco Flandoli

This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.

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Page Count

187

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642182305

ISBN 13

9783642182303

Stochastic Partial Differential Equations in Fluid Mechanics

By: Franco Flandoli,Eliseo Luongo

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Stochastic Partial Differential Equations in Fluid Mechanics

By: Franco Flandoli,Eliseo Luongo

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.

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Page Count

206

Publisher

Springer Nature

Published Date

ISBN 10

9819903858

ISBN 13

9789819903856

SPDE in Hydrodynamics: Recent Progress and Prospects

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005

By: Sergio Albeverio,Franco Flandoli,Yakov G. Sinai

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SPDE in Hydrodynamics: Recent Progress and Prospects

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005

By: Sergio Albeverio,Franco Flandoli,Yakov G. Sinai

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

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183

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Springer Science & Business Media

Published Date

ISBN 10

3540784926

ISBN 13

9783540784920

Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n

By: Franco Flandoli

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Regularity Theory and Stochastic Flows for Parabolic \ISPDES\n

By: Franco Flandoli

First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

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CRC Press

Published Date

ISBN 10

2884490450

ISBN 13

9782884490450

Elementary Symplectic Topology and Mechanics

By: Franco Cardin

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Elementary Symplectic Topology and Mechanics

By: Franco Cardin

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

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Page Count

237

Publisher

Springer

Published Date

ISBN 10

3319110268

ISBN 13

9783319110264

Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

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Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

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