Anuj Kumar

collaborators

2 papers

math.AP2024

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 $\partial_{t} u + U \cdot \nabla u = - \nabla p + ν Δ u$ , where both $U$ and $u$ are divergence-free velocity fields…

math.AP2024

Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field

Elia Bruè, Maria Colombo, Anuj Kumar

Given a divergence-free vector field $u \in L_{t}^{\infty} W_{x}^{1, p} (R^{d})$ and a nonnegative initial datum $ρ_{0} \in L^{r}$ , the celebrated DiPerna--Lions theory established…