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math.AP2026
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 tw…
math.AP2025
A simple proof of linear instability of shear flows with application to vortex sheets
Anuj Kumar, Wojciech OżaÅski
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…
math.AP2025
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}_…