1 citations · 1 across the 6 of their papers we have counts for
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Sharpness of the Osgood Criterion for the Continuity Equation with Divergence-free Vector Fields
Roberto Colombo, Anuj Kumar
For any modulus of continuity that fails the Osgood condition, we construct a divergence-free velocity field for which the associated ODE admits at least two…
A convex integration scheme for the continuity equation past the Sobolev embedding threshold
Maria Colombo, Roberto Colombo, Anuj Kumar
We introduce a convex integration scheme for the continuity equation in the context of the Di Perna-Lions theory that allows to build incompressible vector fields in $C_{t}W^{1,p}_…
Almost anomalous dissipation in advection-diffusion of a divergence-free passive vector
Anuj Kumar
We explore the advection-diffusion of a passive vector described by , where both and are divergence-free velocity fields…
Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity
Elia Bruè, Maria Colombo, Anuj Kumar
We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $…
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…
A simple proof of linear instability of shear flows with application to vortex sheets
Anuj Kumar, Wojciech Ożański
We consider the construction of linear instability of parallel shear flows, which was developed by Zhiwu Lin (SIAM J. Math. Anal. 35(2), 2003). We give an alternative simple proof…