2 citations · 6 across the 6 of their papers we have counts for
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Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field
Elia Bruè, Maria Colombo, Anuj Kumar
Given a divergence-free vector field and a nonnegative initial datum , the celebrated DiPerna--Lions theory established…
Enhanced dissipation for two-dimensional Hamiltonian flows
Elia Bruè, Michele Coti Zelati, Elio Marconi
Let be an autonomous, non-constant Hamiltonian on a compact -dimensional manifold, generating an incompressible velocity field . We give…
Advection diffusion equations with Sobolev velocity field
Elia Bruè, Quoc-Hung Nguyen
In this note we study advection diffusion equations associated to incompressible velocity fields with . We present new estimates on the energy dissipation rate and w…
Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts
Elia Bruè, Quoc-Hung Nguyen
It is known, after \cite{Jabin16} and \cite{AlbertiCrippaMazzucato18}, that ODE flows and solutions of the transport equation associated to Sobolev vector fields do not propagate S…