Density of weak solutions of the fractional Navier-Stokes equations in the smooth divergence-free vector fields

Abstract

In this paper, we consider the fractional Navier-Stokes equations. We extend a previous non-uniqueness result due to Cheskidov and Luo, found in [5], from Navier-Stokes to the fractional case, and from $L^1$-in-time, $W^{1,q}$-in-space solutions for every $q>1$ to $L^s$-in-time, $W^{1,q}$-in-space solutions for appropriate ranges of $s,q$.

arXiv admin note: substantial text overlap with arXiv:2009.06596 by other authors

References in corpus (3)

• Sharp nonuniqueness for the Navier-Stokes equations
• Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
• $L^2$-Density of Wild Initial Data for the Hypodissipative Navier-Stokes Equations