6 problems

The primitive equations are considered with fractional horizontal dissipation exponent $\alpha$, and the currently established global well-posedness result for general initial data…

Consider the dissipative CCF equation and solutions obtained as vanishing-viscosity approximations, with dissipation exponent $\gamma\in[\frac12,1)$. Silvestre–Vicol's Hölder regul…

Consider the two-dimensional Boussinesq system with fractional dissipation exponents $\alpha$ and $\beta$, and let…

Let $u0,theta0 0text{?}$ be initial data in $H^{sigma}(mathbb{R}^2)$ with $sigma2$, and let $u,theta$ solve the 2D Boussinesq system with dissipation exponents $alpha$ and $beta$,…

The model concerns initial data with components $b_j^0$ satisfying the adjacent-scale condition $b_j^0\leq\sqrt{2}b_{j+1}^0$ for sufficiently large indices. Eventual adjacent-scale…

Hmidi's conjecture. The maximum principle should hold for all dimensions $d\ge 1$ and the full range