Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence
DOI10.1007/s40818-023-00162-9arXiv2207.06833MaRDI QIDQ6089031
Maria Colombo, Gianluca Crippa, Massimo Sorella
Publication date: 14 December 2023
Published in: Annals of PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.06833
viscosity solutionmultiplicity of solutionsanomalous dissipationlinear transport theoryscalar theory of turbulenceselection criterium
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) Turbulent transport, mixing (76F25) Initial value problems for second-order parabolic equations (35K15) Initial value problems for linear first-order PDEs (35F10) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Viscosity solutions to PDEs (35D40) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for first-order hyperbolic equations (35L03) Transport equations (35Q49)
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Cites Work
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- Dissipative continuous Euler flows
- Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows
- Non-uniqueness for the transport equation with Sobolev vector fields
- Well-posedness of the transport equation by stochastic perturbation
- Ordinary differential equations, transport theory and Sobolev spaces
- The Euler equations as a differential inclusion
- On vector fields as generators of flows: A counterexample to Nelson's conjecture
- Onsager's conjecture on the energy conservation for solutions of Euler's equation
- Energy dissipation without viscosity in ideal hydrodynamics. I: Fourier analysis and local energy transfer
- Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
- A proof of Onsager's conjecture
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Parabolic equations with irregular data and related issues. Applications to stochastic differential equations
- Strong solutions of stochastic equations with singular time dependent drift
- Nonuniqueness of weak solutions for the transport equation at critical space regularity
- On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity
- Anomalous dissipation in passive scalar transport
- Smoothing does not give a selection principle for transport equations with bounded autonomous fields
- Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
- Stable mixing estimates in the infinite Péclet number limit
- Convex integration solutions to the transport equation with full dimensional concentration
- Loss of regularity for the continuity equation with non-Lipschitz velocity field
- Smooth approximation is not a selection principle for the transport equation with rough vector field
- Non-renormalized solutions to the continuity equation
- Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?
- Anomalous dissipation for \(1/5\)-Hölder Euler flows
- Mixing and un-mixing by incompressible flows
- Diffusion and mixing in fluid flow
- A uniqueness result for the continuity equation in two dimensions
- Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
- Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
- Onsager and the theory of hydrodynamic turbulence
- Onsager's Conjecture for Admissible Weak Solutions
- Energy conservation and Onsager's conjecture for the Euler equations
- The geometry of turbulent advection: sharp estimates for the dimensions of level sets
- The passive scalar spectrum and the Obukhov–Corrsin constant
- Exponential self-similar mixing by incompressible flows
- Dissipation enhancement by mixing
- On the Relation between Enhanced Dissipation Timescales and Mixing Rates
- A stochastic approach to enhanced diffusion
- Turbulent mixing: A perspective
- Structure of level sets and Sard-type properties of Lipschitz maps
- Scalar dissipation rate and dissipative anomaly in isotropic turbulence
- On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence
- Stochastic differential equations. An introduction with applications.
- Tracer microstructure in the large-eddy dominated regime
- Anomalous dissipation for the forced 3D Navier-Stokes equations
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