Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier–Stokes equations
- 2 Time-periodic flow of a viscous liquid past a body
- 3 The Rayleigh–Taylor instability in buoyancy-driven variable density turbulence
- 4 On localization and quantitative uniqueness for elliptic partial differential equations
- 5 Quasi-invariance for the Navier–Stokes equations
- 6 Leray’s fundamental work on the Navier–Stokes equations: a modern review of “Sur le mouvement d’un liquide visqueux emplissant l’espace”
- 7 Stable mild Navier–Stokes solutions by iteration of linear singular Volterra integral equations
- 8 Energy conservation in the 3D Euler equations on T2 × R+
- 9 Regularity of Navier–Stokes flows with bounds for the velocity gradient along streamlines and an effective pressure
- 10 A direct approach to Gevrey regularity on the half-space
- 11 Weak-Strong Uniqueness in Fluid Dynamics
11 - Weak-Strong Uniqueness in Fluid Dynamics
Published online by Cambridge University Press: 15 August 2019
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier–Stokes equations
- 2 Time-periodic flow of a viscous liquid past a body
- 3 The Rayleigh–Taylor instability in buoyancy-driven variable density turbulence
- 4 On localization and quantitative uniqueness for elliptic partial differential equations
- 5 Quasi-invariance for the Navier–Stokes equations
- 6 Leray’s fundamental work on the Navier–Stokes equations: a modern review of “Sur le mouvement d’un liquide visqueux emplissant l’espace”
- 7 Stable mild Navier–Stokes solutions by iteration of linear singular Volterra integral equations
- 8 Energy conservation in the 3D Euler equations on T2 × R+
- 9 Regularity of Navier–Stokes flows with bounds for the velocity gradient along streamlines and an effective pressure
- 10 A direct approach to Gevrey regularity on the half-space
- 11 Weak-Strong Uniqueness in Fluid Dynamics
Summary
We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the one hand, from the instances of nonuniqueness for the Euler equations exhibited in the past years; and on the other hand from the question of convergence of singular limits, for which weak-strong uniqueness represents an elegant tool.
Keywords
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- Chapter
- Information
- Partial Differential Equations in Fluid Mechanics , pp. 289 - 326Publisher: Cambridge University PressPrint publication year: 2018
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