Weak and parabolic solutions of advection-diffusion equations with rough velocity field

DOI10.1007/s00028-023-00919-6arXiv2306.15529OpenAlexW4389822882MaRDI QIDQ6139530

Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa

Publication date: 19 January 2024

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.15529

zbMATH Keywords

advection-diffusion equationtransport/continuity equationdistributional and parabolic solutions

Mathematics Subject Classification ID

PDEs with low regular coefficients and/or low regular data (35R05) Initial value problems for second-order parabolic equations (35K15) Weak solutions to PDEs (35D30) Transport equations (35Q49)

Cites Work

• Unnamed Item
• Unnamed Item
• Non-uniqueness for the transport equation with Sobolev vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Parabolic equations with irregular data and related issues. Applications to stochastic differential equations
• Quantitative stability estimates for Fokker-Planck equations
• 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
• Optimal stability estimates and a new uniqueness result for advection-diffusion equations
• Anomalous dissipation in passive scalar transport
• Convex integration solutions to the transport equation with full dimensional concentration
• Non-renormalized solutions to the continuity equation
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications
• Advection diffusion equations with Sobolev velocity field
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations

This page was built for publication: Weak and parabolic solutions of advection-diffusion equations with rough velocity field