home libri books Fumetti ebook dvd top ten sconti 0 Carrello


Torna Indietro

feireisl eduard; novotný antonín - singular limits in thermodynamics of viscous fluids

Singular Limits in Thermodynamics of Viscous Fluids

;




Disponibilità: Normalmente disponibile in 10 giorni


PREZZO
162,98 €
NICEPRICE
154,83 €
SCONTO
5%



Questo prodotto usufruisce delle SPEDIZIONI GRATIS
selezionando l'opzione Corriere Veloce in fase di ordine.


Pagabile anche con Carta della cultura giovani e del merito, 18App Bonus Cultura e Carta del Docente


Facebook Twitter Aggiungi commento


Spese Gratis

Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 12/2017
Edizione: 2nd ed. 2017





Trama

Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux.

As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.





Sommario

Preface.- 1 Fluid flow modeling.- 1.1 Field equations of continuum fluid mechanics.- 1.2 Constitutive relations.- 2 Mathematical theory of weak solutions.- 2.1 Variational formulation.- 2.2 A priori estimates.- 3 Existence theory.- 3.1 Hypotheses.- 3.2 Structural properties of constitutive functions.- 3.3 Main existence result.- 3.4 Solvability of the approximate system.- 3.5 Limit in the Faedo-Galerkin approximation scheme.- 3.6 Artificial diffusion limit.- 3.7 Vanishing artificial pressure.- 3.8 Regularity properties of weak solutions.- 4 Asymptotic analysis - an introduction.- 4.1 Scaling and scaled equations.- 4.2 Low Mach number limit.- 4.3 Strongly satisfied flows.- 4.4 Acoustic waves.- 5 Singular limits - low stratification.- 5.1 Hypotheses and global existence for the primitive system.- 5.2 Dissipation equation, uniform solutions.- 5.3 Convergence.- 5.4 Acoustiv waves.- 5.5 Conclusion - main result.- 6 Stratified fluids.- 6.1 Motivation.- 6.2 Primitive system.- 6.3 Asymptotic limit.- 6.4 Uniform estimates.- 6.5 Convergence towards the target system.- 6.6 Analysis of the acoustic waves.- 6.7 Asymptotic limit in the entropy balance.- 7 Refined analysis of the acoustic waves.- 7.1 Problem formulation.- 7.2 Main result.- 7.3 Uniform estimates.- 7.4 Analysis of the acoustic waves.- 7.5 Strong convergence of the velocity field.- 8 Appendix.- 8.1 Quasilinear parabolic equations.- 8.2 Mollifiers.- 8.3 The normal traces.- 8.4 The Bogovskii Operator.- 8.5 Maximal regularity to parabolic equations.- 8.6 Korn and Poincaré type inequalities.- 8.7 Radon measures.- 8.8 Weak convergence, monotone and convex functions.- 8.9 Fourier and the Riesz transforms.- 8.10 Div-Curl lemma and commutators involving the Riesz operators.- 8.11 Renormalized solutions to the continuity equation.- 9 Bibliographic remarks 9.1 Fluid flow modeling.- 9.2 Mathematical theory of the weak solutions.- 9.3 Singular limits.










Altre Informazioni

ISBN:

9783319637808

Condizione: Nuovo
Collana: Advances in Mathematical Fluid Mechanics
Dimensioni: 235 x 155 mm Ø 9694 gr
Formato: Copertina rigida
Illustration Notes:XLII, 524 p.
Pagine Arabe: 524
Pagine Romane: xlii


Dicono di noi