6 problems

Mixed conformal-mean curvature boundary data conjecture. The initial boundary value problem for the vacuum Einstein equations is well-posed with respect to the mixed boundary data…

Let $(M,g)$ be a spacetime with timelike boundary ${\mathcal C}$, induced boundary metric $\gamma$, and second fundamental form $A$ of ${\mathcal C}$ in $(M,g)$. Write $[\gamma]$ f…

Let the defocusing nonlinear Schrödinger equation be posed on the half-line. A soliton is a localized coherent structure of the equation. Absence-of-solitons conjecture. The defocu…

Let $Q^\mathrm{D}(t)$ and $Q^\mathrm{N}(t)$ be consistent Dirichlet and Neumann boundary data for the defocusing nonlinear Schrödinger initial-boundary value problem, and let…

Let $L>0$ and consider the initial-boundary value problem for the Korteweg–de Vries equation on $(0,L)\times(0,T)$, with solution space $H^s(0,L)$ and the associated initial and bo…

Consider the one-dimensional quantum hydrodynamic system … for $t>0$ and $x\in[0,1]$, with positive initial density, the Neumann conditions $\rho_x(0,t)=\rho_x(1,t)=0$, and boundar…