An Anisotropic Onsager Criterion for the Two-Dimensional Navier--Stokes Equations with Horizontal Viscosity

Siyu Liang

We consider distributional weak solutions $u\in L_t^{\infty }{L}_x^2$ of the two-dimensional Navier--Stokes equations with horizontal viscosity on ${\mathbb{T}}^2$ or ${\mathbb{R}}^2$, withou…