5 problems

Partial homogenization conjecture. If the corresponding solutions of are denoted by $(\bm{X}^{(k)}_i(t))_{i\in[N_k]}$ and $(\bm{w}^{(k)}_{i,j}(t))_{i,j\in[N_k]}$, then

Let the time-dependent and stationary Navier–Stokes equations be posed on the same domain, with the same time-independent external force, and let the energy of their difference mea…

Invariance conjecture. The measure $\rho_{k/2,R}$ is invariant under a well-defined flow of the Benjamin–Ono equation.

Exponential convergence conjecture. The solutions converge to the constant states

Consider the viscous scalar conservation law … for $t>0$ and $y\in Q$, with initial data $u(0)=u_0$, where $Q$ is either $\mathbb{R}$ or the $N$-dimensional torus $\mathbb{T}^N$, a…