9 problems

Mistretta–Stoppino's conjecture. If

Higher-rank Mistretta–Stoppino conjecture. The following assertions hold: (i) $E$ is linearly (semi)stable; and (ii) $E$ is linearly (semi)stable if and only if $M_E$ is (semi)stab…

Positivity conjecture. For every profile $K(x)$, one has $\nu>0$; consequently, the system admits linearly dispersive waves for all wave numbers $k\in\mathbb{R}$.

Let $\psi^{\mathrm{dat}}$ be data as in the paper's scattering-data definition, with $d>0$ and $N>5$, for the linearised equation on the hypersurface $\Sigma_1$. Let…

Let an $\ell$-boson star have $\ell>1$, and consider non-spherical linearized perturbations, meaning perturbations with nonzero total angular momentum sector. Non-spherical instabi…

Let a nonrelativistic $\ell$-boson star have $\ell\geq3$, and let $\lambda=\lambda_R+i\lambda_I$ be an eigenvalue of the linearized perturbation system, where $\lambda_I$ is its im…

Let $M_1$ be the operator on $V_1$ in the current setting, where $A(x_3)=x_3$, $B(x_3)=\Omega+\lambda_2x_3$, and assume $\Omega>0$. Linear stability conjecture. The evolution group…

An algebraic soliton is a Ricci soliton arising algebraically, including the solvsolitons and nilsolitons considered in the paper. The algebraic soliton linear stability conjecture…

Linear instability conjecture. The equilibrium solutions of all such $G$-Strand equations are linearly unstable.