Advection diffusion equations with Sobolev velocity field
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Publication:2662965
DOI10.1007/s00220-021-03993-4zbMath1461.35046arXiv2003.08198OpenAlexW3132833142MaRDI QIDQ2662965
Publication date: 15 April 2021
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.08198
periodic boundary conditionsenergy dissipation ratepropagation of regularityenhanced dissipation rate
Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Transport equations (35Q49)
Related Items (9)
Endpoint Sobolev theory for the Muskat equation ⋮ Weak and parabolic solutions of advection-diffusion equations with rough velocity field ⋮ Anomalous dissipation for the forced 3D Navier-Stokes equations ⋮ Mixing and diffusion for rough shear flows ⋮ On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity ⋮ On the Cauchy problem for the Muskat equation with non-Lipschitz initial data ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations ⋮ Differentiability in measure of the flow associated with a nearly incompressible BV vector field ⋮ Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem
Cites Work
- Unnamed Item
- Exponential self-similar mixing and loss of regularity for continuity equations
- Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows
- Non-uniqueness for the transport equation with Sobolev vector fields
- Transport equation and Cauchy problem for BV vector fields
- Ordinary differential equations, transport theory and Sobolev spaces
- A quantitative theory for the continuity equation
- On the Sobolev space of functions with derivative of logarithmic order
- Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts
- Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
- Separation of time-scales in drift-diffusion equations on \(\mathbb{R}^2\)
- Convex integration solutions to the transport equation with full dimensional concentration
- Loss of regularity for the continuity equation with non-Lipschitz velocity field
- Convergence of numerical approximations to non-linear continuity equations with rough force fields
- Universal mixers in all dimensions
- Non-renormalized solutions to the continuity equation
- Mixing and un-mixing by incompressible flows
- Diffusion and mixing in fluid flow
- A lemma and a conjecture on the cost of rearrangements
- Critical non-Sobolev regularity for continuity equations with rough velocity fields
- Estimates and regularity results for the DiPerna-Lions flow
- A new approach to bounds on mixing
- Diffusion-limited mixing by incompressible flows
- Exponential self-similar mixing by incompressible flows
- Dissipation enhancement by mixing
- Optimal stability estimates for continuity equations
- Qnique Continuation for
- On the Relation between Enhanced Dissipation Timescales and Mixing Rates
- Continuity equations and ODE flows with non-smooth velocity
- Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows
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