V. Giri

activity

20242026

collaborators

6 papers

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.AP2025

Non-uniqueness of HÃ¶lder continuous solutions for Inhomogeneous Incompressible Euler flows

Vikram Giri, Ujjwal Koley

We consider the inhomogeneous (or density dependent) incompressible Euler equations in a three-dimensional periodic domain. We construct density $ϱ$ and velocity $u$ such tha…

math.MG2025

A step towards the tensorization of Sobolev spaces

Silvia Ghinassi, Vikram Giri, Elisa Negrini

We prove that Sobolev spaces on Cartesian and warped products of metric spaces tensorize, only requiring that one of the factors is a doubling space supporting a PoincarÃ© inequali…

math.AP2025

The $L^{3}$ -based strong Onsager theorem

Vikram Giri, Hyunju Kwon, Matthew Novack

In this work, we prove the $L^{3}$ -based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate…

math.CO2025

The structure of Lonely Runner spectra

Vikram Giri, Noah Kravitz

For each subtorus $T$ of $(R / Z)^{n}$ , let $D (T)$ denote the (infimal) $L^{\infty}$ -distance from $T$ to the point $(1/2, \dots, 1/2)$ . The $n$ -th Lonely Runner spectr…

math.AP2024

The Onsager conjecture in 2D: a Newton-Nash iteration

Vikram Giri, Razvan-Octavian Radu

For any $I^^{3} < 1/3$ , we construct a nontrivial weak solution $u$ to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies $u\in C^Î³(\ma…