4 citations · 5 across the 2 of their papers we have counts for
6 papers · 1 filter
Regularity properties of passive scalars with rough divergence-free drifts
Dallas Albritton, Hongjie Dong
We present sharp conditions on divergence-free drifts in Lebesgue spaces for the passive scalar advection-diffusion equation \[ \partial_t θ- Δθ+ b \cdot \nabla θ= 0 \] to satisfy…
Enhanced dissipation and Hörmander's hypoellipticity
Dallas Albritton, Rajendra Beekie, Matthew Novack
We examine the phenomenon of enhanced dissipation from the perspective of Hörmander's classical theory of second order hypoelliptic operators [31]. Consider a passive scalar in a s…
Long-time behavior of scalar conservation laws with critical dissipation
Dallas Albritton, Rajendra Beekie
The critical Burgers equation is a toy model for the competition between transport and diffusion with regard to shock formation in fluids.…
Localised necessary conditions for singularity formation in the Navier-Stokes equations with curved boundary
Dallas Albritton, Tobias Barker
We generalize two results in the Navier-Stokes regularity theory whose proofs rely on `zooming in' on a presumed singularity to the local setting near a curved portion $Γ\subset \p…
On local Type I singularities of the Navier-Stokes equations and Liouville theorems
Dallas Albritton, Tobias Barker
We prove that suitable weak solutions of the Navier-Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying…
Global weak Besov solutions of the Navier-Stokes equations and applications
Dallas Albritton, Tobias Barker
We introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $\dot{B}^{-1+\frac{3}{…