7 problems

Long-time equilibrium conjecture. The one-dimensional solution should satisfy

Consider one-dimensional dispersive flows on the real line with cubic conservative nonlinearities and initial data of size $epsilon \ll 1$. Non-localized data long-time well-posedn…

Let $S(t,x)$, $I(t,x)$, and $R(t,x)$ denote the susceptible, infected, and recovered population densities in the heterogeneous SIRS model, and let $\lambda$ and $\Lambda_0$ be the…

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain with smooth boundary, and consider the parabolic problem (CC8) with positive parameters $\beta$ and constant $\gamma$. For a tra…

Let $G_t$ be a solution of the renormalized Boltzmann equation obtained by anisotropic rescaling, preserving its mass, energy, and second moments. Long-time convergence conjecture.…

Let the nonlinear problem and its corresponding linear problem be given, and consider solutions arising from sufficiently small initial data. Asymptotic linearization conjecture. F…

Let ${k_0}<2$, and let $g(t,x)$ denote the solution in the original variables for the mass-aggregation model. Pointwise-limit conjecture. There exists a limit function…