4 papers · 1 filter
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…
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(\ma…