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  • Produktbild: The Navier-Stokes Equations
  • Produktbild: The Navier-Stokes Equations

The Navier-Stokes Equations An Elementary Functional Analytic Approach

Aus der Reihe Birkhäuser Advanced Texts Basler Lehrbücher

Fr. 112.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

23.08.2014

Verlag

Springer Basel

Seitenzahl

367

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

599 g

Auflage

Softcover reprint of the original 1st ed. 2001

Sprache

Englisch

ISBN

978-3-0348-9493-7

Beschreibung

Rezension

"The book is written in a well-arranged way, easy to survey and with utilization of the newest results..it is [written] for an extensive circle of readers, from students to experts…and specialists in the field."


--Zentralblatt Math

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

23.08.2014

Verlag

Springer Basel

Seitenzahl

367

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

599 g

Auflage

Softcover reprint of the original 1st ed. 2001

Sprache

Englisch

ISBN

978-3-0348-9493-7

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: The Navier-Stokes Equations
  • Produktbild: The Navier-Stokes Equations
  • I Introduction.- 1 Basic notations.- 1.1 The equations of Navier-Stokes.- 1.2 Further notations.- 1.3 Linearized equations.- 2 Description of the functional analytic approach.- 2.1 The role of the Stokes operator A.- 2.2 The stationary linearized case.- 2.3 The stationary nonlinear case.- 2.4 The nonstationary linearized case.- 2.5 The full nonlinear case.- 3 Function spaces.- 3.1 Smooth functions.- 3.2 Smoothness properties of the boundary ??.- 3.3 Lq-spaces.- 3.4 The boundary spaces Lq (??).- 3.5 Distributions.- 3.6 Sobolev spaces.- II Preliminary Results.- 1 Embedding properties and related facts.- 1.1 Poincaré inequalities.- 1.2 Traces and Green’s formula.- 1.3 Embedding properties.- 1.4 Decomposition of domains.- 1.5 Compact embeddings.- 1.6 Representation of functionals.- 1.7 Mollification method.- 2 The operators ? and div.- 2.1 Solvability of div v = g and ?p = f.- 2.2 A criterion for gradients.- 2.3 Regularity results on div v = g.- 2.4 Further results on the equation div v = g.- 2.5 Helmholtz decomposition in L2-spaces.- 3 Elementary functional analytic properties.- 3.1 Basic facts on Banach spaces.- 3.2 Basic facts on Hilbert spaces.- 3.3 The Laplace operator ?.- 3.4 Resolvent and Yosida approximation.- III The Stationary Navier-Stokes Equations.- 1 Weak solutions of the Stokes equations.- 1.1 The notion of weak solutions.- 1.2 Embedding properties of $$\widehat W_{0,\sigma }^{1,2}(\Omega )$$.- 1.3 Existence of weak solutions.- 1.4 The nonhomogeneous case div u = g.- 1.5 Regularity properties of weak solutions.- 2 The Stokes operator A.- 2.1 Definition and properties.- 2.2 The square root $$
    A^{\tfrac{1}
    {2}}
    $$ of A.- 2.3 The Stokes operator A in ?n.- 2.4 Embedding properties of D(A?).- 2.5 Completion of the space D(A?).- 2.6 The operator $$
    A^{ - \tfrac{1}
    {2}}
    $$P div.- 3 The stationary Navier-Stokes equations.- 3.1 Weak solutions.- 3.2 The nonlinear term u · ?u.- 3.3 The associated pressure p.- 3.4 Existence of weak solutions in bounded domains.- 3.5 Existence of weak solutions in unbounded domains.- 3.6 Regularity properties for the stationary nonlinear system.- 3.7 Some uniqueness results.- IV The Linearized Nonstationary Theory.- 1 Preliminaries for the time dependent linear theory.- 1.1 The nonstationary Stokes system.- 1.2 Basic spaces for the time dependent theory.- 1.3 The vector valued operator $$
    \tfrac{d}
    {{dt}}
    $$.- 1.4 Time dependent gradients ?p.- 1.5 A special solution class of the homogeneous system.- 1.6 The inhomogeneous evolution equation u? + Au = f.- 2 Theory of weak solutions in the linearized case.- 2.1 Weak solutions.- 2.2 Equivalent formulation and approximation.- 2.3 Energy equality and strong continuity.- 2.4 Representation formula for weak solutions.- 2.5 Basic estimates of weak solutions.- 2.6 Associated pressure of weak solutions.- 2.7 Regularity properties of weak solutions.- V The Full Nonlinear Navier-Stokes Equations.- 1 Weak solutions.- 1.1 Definition of weak solutions.- 1.2 Properties of the nonlinear term u · ?u.- 1.3 Integral equation for weak solutions and weak continuity.- 1.4 Energy equality and strong continuity.- 1.5 Serrin's uniqueness condition.- 1.6 Integrability properties of weak solutions in space and time,the scale of Serrin's quantity.- 1.7 Associated pressure of weak solutions.- 1.8 Regularity properties of weak solutions.- 2 Approximation of the Navier-Stokes equations.- 2.1 Approximate Navier-Stokes system.- 2.2 Properties of approximate weak solutions.- 2.3 Regularity properties of approximate weak solutions.- 2.4 Smooth solutions of the Navier-Stokes equationswith “slightly” modified forces.- 2.5 Existence of approximate weak solutions.- 2.6 Uniform norm bounds of approximate weak solutions.- 3 Existence of weak solutions of the Navier-Stokes system.- 3.1 Main result.- 3.2 Preliminary compactness results.- 3.3 Proof of Theorem 3.1.1.- 3.4 Weighted energy inequalities and time decay.- 3.5 Exponential decay for domains for which thePoincarü inequality holds.- 3.6 Generalized energy inequality.- 4 Strong solutions of the Navier-Stokes system.- 4.1 The notion of strong solutions.- 4.2 Existence results.