Matthew Novack

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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.AP2025

Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces

Estepan Ashkarian, Ataleshvara Bhargava, Nicholas Gismondi +1

In this paper we construct non-trivial solutions to the stationary Navier-Stokes equations on the two dimensional torus which lie in $\bigcap_{ε\in (0,1)} L^{2-ε}(\mathbb{T}^2) \ca…