Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions
Abstract
We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in albritton2021non, the solutions we construct live at a supercritical scaling, in which the hypodissipation formally becomes negligible as t 0+. In this scaling, it is possible to perturb the Euler non-uniqueness scenario of Vishik Vishik1,Vishik2 to the hypodissipative setting at the nonlinear level. Our perturbation argument is quasilinear in spirit and circumvents the spectral theoretic approach to incorporating the dissipation in albritton2021non.
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