3 problems

Weak asymptotic decomposition conjecture. The solution admits a decomposition

Let $\rho>0$ be a mass, let the initial datum have mass $\rho$ and momentum $0$, and let $g_t$ be the associated solution in rescaled variables. Let $G_\rho$ be the steady state of…

Let $G_\rho$ denote a self-similar profile with mass $\rho>0$ and momentum $0$. Uniqueness conjecture. For any mass $\rho>0$, the self-similar profile $G_\rho$ with mass $\rho$ and…