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| Author | : Peter Constantin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 79 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821823159 |
The purpose of this article is to fill some part of the gap existing between the mathematical theory of the Navier-Stokes equations and the conventional theory of turbulence and to provide a rigorous connection between these theories.
| Author | : Boling Guo |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 438 |
| Release | : 2018-07-09 |
| Genre | : Mathematics |
| ISBN | : 3110549425 |
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
| Author | : Carlo Marchioro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 295 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242843 |
Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi cult new mathematical {::oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.
| Author | : Journal of Nonlinear Science |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 533 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461212464 |
Starting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community.
| Author | : Juan Carlos Simo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 546 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780387986630 |
This collection of papers in honour of Juan-Carlos Simo cover subjects including: dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods; gravity waves on the surface of the sphere; and problems and progress in microswimming.
| Author | : Roger Temam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 517 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468403133 |
This is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.
| Author | : M. Lesieur |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 566 |
| Release | : 2003-07-01 |
| Genre | : Science |
| ISBN | : 3540456740 |
Following a longstanding tradition of the Les Houches Summer Schools, this book uses a pedagogically presented and accessible style to treat 2D and 3D turbulence from the experimental, theoretical and computational points of view.
| Author | : Felix E. Browder |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 591 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821814729 |
| Author | : Andrew J. Majda |
| Publisher | : Springer |
| Total Pages | : 97 |
| Release | : 2016-09-14 |
| Genre | : Mathematics |
| ISBN | : 3319322176 |
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.
| Author | : James C. Robinson |
| Publisher | : Cambridge University Press |
| Total Pages | : 488 |
| Release | : 2001-04-23 |
| Genre | : Mathematics |
| ISBN | : 9780521632041 |
This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.
