Mathematical Theory of Incompressible Nonviscous Fluids PDF Download
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Author: Carlo Marchioro
Publisher: Springer Science & Business Media
ISBN: 9780387940441
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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: Carlo Marchioro
Publisher: Springer Science & Business Media
ISBN: 9780387940441
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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: Carlo Marchioro
Publisher:
ISBN: 9787506240727
Category : Fluid dynamics
Languages : en
Pages : 283
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Book Description
Author: Carlo Marchioro
Publisher: Springer Science & Business Media
ISBN: 1461242843
Category : Mathematics
Languages : en
Pages : 295
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Book Description
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: Radyadour K. Zeytounian
Publisher: Springer Science & Business Media
ISBN: 3642562159
Category : Technology & Engineering
Languages : en
Pages : 302
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Book Description
From the reviews: "Researchers in fluid dynamics and applied mathematics will enjoy this book for its breadth of coverage, hands-on treatment of important ideas, many references, and historical and philosophical remarks." Mathematical Reviews
Author: Olʹga Aleksandrovna Ladyzhenskai︠a︡
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 252
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Book Description
Author: Sir Horace Lamb
Publisher:
ISBN:
Category : Hydrodynamics
Languages : en
Pages : 612
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Book Description
Author: Hideo Kozono
Publisher:
ISBN:
Category : Fluid dynamics
Languages : en
Pages : 288
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Book Description
Author: Radyadour Kh. Zeytounian
Publisher: Springer Science & Business Media
ISBN: 3662104474
Category : Science
Languages : en
Pages : 498
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Book Description
This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.
Author: Tobias Hansel
Publisher:
ISBN: 9783832530952
Category :
Languages : en
Pages : 0
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Book Description
In the mathematical theory of viscous incompressible fluids the fundamental model is provided by the incompressible Navier-Stokes equations. For the last 20 years the analysis of the Navier-Stokes equations in the exterior of a moving and rotating obstacle has attracted particular attention. The main difficulty in this context arises from the fact that a linear coordinate transformation, which is used to handle the moving domain, results in transformed fluid equations that contain a drift term with linearly growing, hence unbounded coefficients. In this thesis the Navier-Stokes equations in the exterior of a moving, in particular rotating, obstacle are studied and the main emphasis is placed on the case where the obstacle undergoes a rotation described by a non-autonomous equation, and on fluids with variable density. In the non-autonomous case an appropriate functional analytic framework is adopted to show existence and uniqueness of local mild solutions. Moreover, based on the Faedo-Galerkin method and suitable a priori estimates, a well-posedness result for incompressible fluids with variable density is proved. For the proof new techniques needed to be developed. In particular, new elliptic estimates for the modified stationary Stokes problem with rotating effect are derived.
Author: O. A. Ladyženskaja
Publisher:
ISBN:
Category :
Languages : en
Pages : 184
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Book Description
