UID:
almafu_9960161224302883
Umfang:
1 online resource (288 pages) :
,
illustrations, tables.
Ausgabe:
First edition.
ISBN:
9780128110454
,
0128110457
Serie:
Mathematics in Science and Engineering
Inhalt:
Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs. Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness
Anmerkung:
Front Cover -- Existence Theory for Generalized Newtonian Fluids -- Copyright -- Contents -- Preface -- Acknowledgment -- Notation -- Part 1 Stationary problems -- 1 Preliminaries -- 1.1 Lebesgue & -- Sobolev spaces -- 1.2 Orlicz spaces -- 1.3 Basics on Lipschitz truncation -- 1.4 Existence results for power law uids -- 2 Fluid mechanics & -- Orlicz spaces -- 2.1 Bogovskii operator -- 2.2 Negative norms & -- the pressure -- 2.3 Sharp conditions for Korn-type inequalities -- 3 Solenoidal Lipschitz truncation -- 3.1 Solenoidal truncation - stationary case -- 3.2 Solenoidal Lipschitz truncation in 2D -- 3.3 A-Stokes approximation - stationary case -- 4 Prandtl-Eyring uids -- 4.1 The approximated system -- 4.2 Stationary ows -- Part 2 Non-stationary problems -- 5 Preliminaries -- 5.1 Bochner spaces -- 5.2 Basics on parabolic Lipschitz truncation -- 5.3 Existence results for power law uids -- 6 Solenoidal Lipschitz truncation -- 6.1 Solenoidal truncation - evolutionary case -- 6.2 A-Stokes approximation - evolutionary case -- 7 Power law uids -- 7.1 The approximated system -- 7.2 Non-stationary ows -- Part 3 Stochastic problems -- 8 Preliminaries -- 8.1 Stochastic processes -- 8.2 Stochastic integration -- 8.3 Itô's Lemma -- 8.4 Stochastic ODEs -- 9 Stochastic PDEs -- 9.1 Stochastic analysis in in nite dimensions -- 9.2 Stochastic heat equation -- 9.3 Tools for compactness -- 10 Stochastic power law uids -- 10.1 Pressure decomposition -- 10.2 The approximated system -- 10.3 Non-stationary ows -- A Function spaces -- A.1 Function spaces involving the divergence -- A.2 Function spaces involving symmetric gradients -- B The A-Stokes system -- B.1 The stationary problem -- B.2 The non-stationary problem -- B.3 The non-stationary problem in divergence form -- C Itô's formula in in nite dimensions -- References -- Index -- Back Cover.
Weitere Ausg.:
ISBN 9780128110447
Weitere Ausg.:
ISBN 0128110449
Sprache:
Englisch
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