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The Resource Lecture notes on regularity theory for the Navier-Stokes equations, Gregory Seregin

Lecture notes on regularity theory for the Navier-Stokes equations, Gregory Seregin

Label
Lecture notes on regularity theory for the Navier-Stokes equations
Title
Lecture notes on regularity theory for the Navier-Stokes equations
Statement of responsibility
Gregory Seregin
Creator
Author
Subject
Genre
Language
eng
Summary
The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value
Member of
Cataloging source
N$T
http://library.link/vocab/creatorDate
1950-
http://library.link/vocab/creatorName
Seregin, Gregory
Dewey number
515/.353
Index
index present
LC call number
QA377
LC item number
.S463 2014eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Navier-Stokes equations
  • Fluid dynamics
  • MATHEMATICS
  • MATHEMATICS
  • Fluid dynamics
  • Navier-Stokes equations
Label
Lecture notes on regularity theory for the Navier-Stokes equations, Gregory Seregin
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions
  • 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions
  • Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index
Control code
894894804
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9789814623414
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)894894804
Label
Lecture notes on regularity theory for the Navier-Stokes equations, Gregory Seregin
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions
  • 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions
  • Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index
Control code
894894804
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9789814623414
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)894894804

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      38.710138 -90.311107
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