Author: Dongho ChaePublisher:
ISBN:
Category :
Languages : en
Pages : 18
Book Description
A Type of Gevrey Class Regularity of Weak Solutions of the Navier-stokes Equations
Author: Dongho ChaeOn the Interior Regularity of Weak Solutions of the Navier-stokes Equations
Author: James SerrinPublisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 40
Book Description
Remarks on the Regularity of Weak Solutions of the Navier-Stokes Equations
Author: Dongho ChaePublisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 21
Book Description
On the Regularity of Weak Solutions of the Equations of Navier-Stokes
Author: H. SohrNavier–Stokes Equations
Author: Grzegorz ŁukaszewiczPublisher: Springer
ISBN: 331927760X
Category : Mathematics
Languages : en
Pages : 395
Book Description
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
The Three-Dimensional Navier-Stokes Equations
Author: James C. RobinsonPublisher: Cambridge University Press
ISBN: 1107019664
Category : Mathematics
Languages : en
Pages : 487
Book Description
An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
The Stokes and Navier–Stokes Equations in Exterior Domains
Author: David WegmannPublisher: Logos Verlag Berlin GmbH
ISBN: 3832548394
Category : Juvenile Nonfiction
Languages : en
Pages : 131
Book Description
In the first part of this thesis we established a maximal regularity result to the Stokes equations in exterior domains with moving boundary. This leads to existence of solutions to the Navier–Stokes equations globally in time for small data. Secondly, we consider Leray's problem on the decay of weak solutions to the Navier–Stokes equations in an exterior domain with non-homogeneous Dirichlet boundary data. It is shown that the solution decays polynomially.
Local Regularity of Suitable Weak Solutions to the Navier-Stokes Equations Near the Boundary
Author: Grigorij A. SereginCritical Parabolic-Type Problems
Author: Tomasz W. DłotkoPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 311059868X
Category : Mathematics
Languages : en
Pages : 217
Book Description
This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
Navier-Stokes Equations and Turbulence
Author: C. FoiasPublisher: Cambridge University Press
ISBN: 1139428993
Category : Science
Languages : en
Pages : 363
Book Description
This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.