Norm growth, non-uniqueness, and anomalous dissipation in passive scalars

Smoothness and regularity of solutions to PDEs (35B65) Turbulent transport, mixing (76F25) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Transport equations (35Q49)

Cites Work

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Ordinary differential equations, transport theory and Sobolev spaces
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
Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations
Diffusion and mixing in fluid flow
A uniqueness result for the continuity equation in two dimensions
Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box
Exponential self-similar mixing by incompressible flows
Classical and Multilinear Harmonic Analysis
The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number
On the Relation between Enhanced Dissipation Timescales and Mixing Rates
Turbulent mixing: A perspective
INTERPOLATION OF HILBERT AND SOBOLEV SPACES: QUANTITATIVE ESTIMATES AND COUNTEREXAMPLES
Scalar dissipation rate and dissipative anomaly in isotropic turbulence
On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence
Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence
Anomalous dissipation for the forced 3D Navier-Stokes equations
Onsager critical solutions of the forced Navier-Stokes equations

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