A remark on selection of solutions for the transport equation

Cites Work

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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
Functional analysis, Sobolev spaces and partial differential equations
Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
Positive solutions of transport equations and classical nonuniqueness of characteristic curves
On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity
Smoothing does not give a selection principle for transport equations with bounded autonomous fields
Convex integration solutions to the transport equation with full dimensional concentration
Concerning the pathological set in the context of probabilistic well-posedness
Smooth approximation is not a selection principle for the transport equation with rough vector field
A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\)
Non-renormalized solutions to the continuity equation
Random Data Wave Equations
Continuity equations and ODE flows with non-smooth velocity
Hyperbolic Conservation Laws in Continuum Physics
The Bair category method for intermittent convex integration
Nonlinear PDE in the presence of singular randomness
Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields
On the failure of the chain rule for the divergence of Sobolev vector fields
Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence

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