7 problems

Let $\theta\in[-1,1]$, let $\mathbb V^k$ be either $\mathbb Q^k$ or $\mathbb P^k$, and let $\mathbb V^k_+$ denote the corresponding cone of positive polynomials. For…

Let $\theta\in[-1,1]$ and let $\mathbb V^k$ denote either the tensor-product polynomial space $\mathbb Q^k$ or the total-degree polynomial space $\mathbb P^k$, with…

Let two compatible jamitons be given, with their parameters describing their densities, velocities, and lengths. Unique post-collision jamiton conjecture. The collision of two comp…

Algebraic stability conjecture. The operator $\Omega(k)$ has negative eigenvalues if and only if $\lambda_{\ell,1}<0$ for every $\ell=1,\ldots,N$.

Stability conjecture. If the eigenvalues of all four stability operators are negative for every wavenumber $k$, then the system (1.2) is stable.

Uniqueness and classification conjecture. The solution of the Riemann problem consisting of the governing equations and initial condition is unique for any given $\gamma$ and…

Let $d\geq 2$ and consider a $d$-dimensional nonlinear symmetric system that is totally linearly degenerate. Suppose the initial data belong to $H^s(\mathbb{R}^d)$ with…