Holder continuous Euler flows in three dimensions with compact support in time /

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Isett, Philip
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton University Press, 2017.
Colección:Annals of mathematics studies ; no. 196.
Temas:
Fluid dynamics > Mathematics.
Dynamique des fluides > Mathématiques.
TECHNOLOGY & ENGINEERING > Hydraulics.
Beltrami flows.
Einstein summation convention.
Euler equations.
Euler flow.
Euler-Reynolds equations.
Euler-Reynolds system.
Galilean invariance.
Galilean transformation.
Hlder norm.
Hlder regularity.
Lars Onsager.
Main Lemma.
Main Theorem.
Mollification term.
Newton's law.
Noether's theorem.
Onsager's conjecture.
Reynolds stres.
Reynolds stress.
Stress equation.
Stress term.
Transport equation.
Transport term.
Transport-Elliptic equation.
abstract index notation.
algebra.
amplitude.
coarse scale flow.
coarse scale velocity.
coefficient.
commutator estimate.
commutator term.
commutator.
conservation of momentum.
continuous solution.
contravariant tensor.
convergence.
convex integration.
correction term.
correction.
covariant tensor.
dimensional analysis.
divergence equation.
divergence free vector field.
divergence operator.
energy approximation.
energy function.
energy increment.
energy regularity.
energy variation.
energy.
error term.
error.
finite time interval.
first material derivative.
fluid dynamics.
frequencies.
frequency energy levels.
h-principle.
integral.
lifespan parameter.
lower indices.
material derivative.
mollification.
mollifier.
moment vanishing condition.
momentum.
multi-index.
non-negative function.
nonzero solution.
optimal regularity.
oscillatory factor.
oscillatory term.
parameters.
parametrix expansion.
parametrix.
phase direction.
phase function.
phase gradient.
pressure correction.
pressure.
regularity.
relative acceleration.
relative velocity.
scaling symmetry.
second material derivative.
smooth function.
smooth stress tensor.
smooth vector field.
spatial derivative.
stress.
tensor.
theorem.
time cutoff function.
time derivative.
transport derivative.
transport equations.
transport estimate.
transport.
upper indices.
vector amplitude.
velocity correction.
velocity field.
velocity.
weak limit.
weak solution.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Preface
  • Part I. Introduction
  • Part II. General Considerations of the Scheme
  • Part III. Basic Construction of the Correction
  • Part IV. Obtaining Solutions from the Construction
  • Part V. Construction of Regular Weak Solutions: Preliminaries
  • Part VI Construction of Regular Weak Solutions: Estimating the Correction
  • Part VII. Construction of Regular Weak Solutions: Estimating the New Stress
  • Acknowledgments
  • Appendices
  • References
  • Index

Ejemplares similares