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arXiv · 2209.08713

Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions

Dallas Albritton·Maria Colombo
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Abstract

We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in which the hypodissipation formally becomes negligible as $t \to 0^+$. In this scaling, it is possible to perturb the Euler non-uniqueness scenario of Vishik \cite{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 \cite{albritton2021non}.

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Dallas Albritton, Maria Colombo. 2022-09-19. Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions. https://doi.org/10.1007/s00220-023-04725-6

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