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ISBN 10: 0691249547 ISBN 13: 9780691249544
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Aggiungi al carrelloPaperback. Condizione: New. A new threshold for the existence of weak solutions to the incompressible Euler equationsTo gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.
Lingua: Inglese
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ISBN 10: 0691249547 ISBN 13: 9780691249544
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Lingua: Inglese
Editore: Springer International Publishing, Springer Nature Switzerland Sep 2020, 2020
ISBN 10: 3030548988 ISBN 13: 9783030548988
Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Aggiungi al carrelloTaschenbuch. Condizione: Neu. Neuware -This volume brings together four contributions to mathematical fluid mechanics, a classical but still highly active research field. The contributions cover not only the classical Navier-Stokes equations and Euler equations, but also some simplified models, and fluids interacting with elastic walls. The questions addressed in the lectures range from the basic problems of existence/blow-up of weak and more regular solutions, to modeling and aspects related to numerical methods.This book covers recent advances in several important areas of fluid mechanics. An output of the CIME Summer School 'Progress in mathematical fluid mechanics' held in Cetraro in 2019, it offers a collection of lecture notes prepared by T. Buckmaster, (Princeton), S. Canic (UCB) P. Constantin (Princeton) and A. Kiselev (Duke).These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 172 pp. Englisch.
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Editore: Springer International Publishing, 2020
ISBN 10: 3030548988 ISBN 13: 9783030548988
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Aggiungi al carrelloTaschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume brings together four contributions to mathematical fluid mechanics, a classical but still highly active research field. The contributions cover not only the classical Navier-Stokes equations and Euler equations, but also some simplified models, and fluids interacting with elastic walls. The questions addressed in the lectures range from the basic problems of existence/blow-up of weak and more regular solutions, to modeling and aspects related to numerical methods.This book covers recent advances in several important areas of fluid mechanics. An output of the CIME Summer School 'Progress in mathematical fluid mechanics' held in Cetraro in 2019, it offers a collection of lecture notes prepared by T. Buckmaster, (Princeton), S. Canic (UCB) P. Constantin (Princeton) and A. Kiselev (Duke).These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics.
Lingua: Inglese
Editore: Princeton University Press, US, 2023
ISBN 10: 0691249547 ISBN 13: 9780691249544
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Aggiungi al carrelloPaperback. Condizione: New. A new threshold for the existence of weak solutions to the incompressible Euler equationsTo gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been used to produce solutions with precise regularity, which are necessary for the resolution of the Onsager conjecture for the 3D Euler equations, or solutions with intermittency, which are necessary for the construction of dissipative weak solutions for the Navier-Stokes equations. In this book, weak solutions to the 3D Euler equations are constructed for the first time with both non-negligible regularity and intermittency. These solutions enjoy a spatial regularity index in L^2 that can be taken as close as desired to 1/2, thus lying at the threshold of all known convex integration methods. This property matches the measured intermittent nature of turbulent flows. The construction of such solutions requires technology specifically adapted to the inhomogeneities inherent in intermittent solutions. The main technical contribution of this book is to develop convex integration techniques at the local rather than global level. This localization procedure functions as an ad hoc wavelet decomposition of the solution, carrying information about position, amplitude, and frequency in both Lagrangian and Eulerian coordinates.
Lingua: Inglese
Editore: Princeton University Press, 2023
ISBN 10: 0691249547 ISBN 13: 9780691249544
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Aggiungi al carrelloCondizione: New. Über den AutorTristan Buckmaster is professor of mathematics at the University of Maryland. Nader Masmoudi is professor of mathematics at New York University. Matthew Novack is assistant professor of mathematics.
Lingua: Inglese
Editore: Princeton University Press, 2023
ISBN 10: 0691249555 ISBN 13: 9780691249551
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