10 citations · 24 across the 10 of their papers we have counts for
11 papers
Non-conservation of a generalized helicity in the Euler equations
Vikram Giri, Hyunju Kwon, Matthew Novack
For a solution to the incompressible 3D Euler equations, the helicity is constant in time. For general low-r…
Non-uniqueness of Hölder 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 and velocity such tha…
The -based strong Onsager theorem
Vikram Giri, Hyunju Kwon, Matthew Novack
In this work, we prove the -based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate…
A wavelet-inspired -based convex integration framework for the Euler equations
Vikram Giri, Hyunju Kwon, Matthew Novack
In this work, we develop a wavelet-inspired, -based convex integration framework for constructing weak solutions to the three-dimensional incompressible Euler equations. The m…
The Onsager conjecture in 2D: a Newton-Nash iteration
Vikram Giri, Razvan-Octavian Radu
For any , we construct a nontrivial weak solution to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies $u\in C^γ(\math…
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 Poincaré inequalit…
The structure of Lonely Runner spectra
Vikram Giri, Noah Kravitz
For each subtorus of , let denote the (infimal) -distance from to the point . The -th Lonely Runner spectr…
Instability and nonuniqueness for the Euler equations in vorticity form, after M. Vishik
Dallas Albritton, Elia Brué, Maria Colombo +4
In this expository work, we present Vishik's theorem on non-unique weak solutions to the two-dimensional Euler equations on the whole space, \[ \partial_t ω+ u \cdot \nabla ω= f \,…
On Non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations
Vikram Giri, Hyunju Kwon
We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density aw…
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…
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 (and of a nonautonomous bounded divergence free vector field in ) and of a bou…