4 problems

K41–Onsager conjecture for Navier–Stokes. There exists a finite open interval $I$ and a sequence of suitable weak solutions $v_{\nu_j}$ with $\nu_j\to0$ that is uniformly bounded i…

Let $u$ solve the two-dimensional Navier–Stokes equations with viscosity $u$, and let $\overline{u}$ denote the corresponding Euler solution. Suppose the vanishing viscosity limit…

Let $\theta_0$ satisfy the hypotheses of the Hölder $1/2$ a priori estimate conjecture, and let $\theta$ be a vanishing-viscosity limit of solutions of … Here…

Let $M\ne0$, $\varepsilon\in(0,1)$, and consider the transport-diffusion equation on $(0,T)\times(0,L)$, … with boundary control at $x=0$, homogeneous boundary condition at $x=L$,…