V. Giri

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math.AP2026

Non-conservation of a generalized helicity in the Euler equations

Vikram Giri, Hyunju Kwon, Matthew Novack

For a $C_{t, x}^{1}$ solution $u$ to the incompressible 3D Euler equations, the helicity $H (u (t)) = \int_{T^{3}} u \cdot curl u$ is constant in time. For general low-r…

math.AP2021

Non-uniqueness of integral curves for autonomous Hamiltonian vector fields

Vikram Giri, Massimo Sorella

In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport equation has non-unique pos…

math.AP2020

Smoothing does not give a selection principle for transport equations with bounded autonomous fields

Camillo De Lellis, Vikram Giri

We give an example of a bounded divergence free autonomous vector field in $R^{3}$ (and of a nonautonomous bounded divergence free vector field in $R^{2}$ ) and of a bou…