6 problems

The 2D quasi-geostrophic equation is considered with an initial scalar field whose level sets are of hyperbolic saddle type. Constantin–Majda–Tabak conjecture. Such a solution is l…

Consider the original three-dimensional incompressible axisymmetric Navier–Stokes equations and the possibility of focusing blowup at the symmetry axis $r=0$. Two-scale blowup excl…

Consider the three-dimensional Euler solution arising from the same initial data used in the comparison computations described in Cases 1 and 3. Finite-time singularity conjecture.…

Let the three-dimensional incompressible Euler equations be equipped with Kida's high-symmetry initial data. Boratav–Pelz conjecture. The Euler equations with these initial data sh…

Let $d$ be the director field in the three-dimensional nematic liquid crystal flow, and define the stress tensor … Under the same assumptions as the finite-time singularity theorem…

Consider the two-dimensional surface quasi-geostrophic equation … with $u=\mathcal R^\perp\theta$, where $\theta$ is the active scalar and the geometry of its level sets contains a…