9 problems

Let ${\mathbf P}$ be the space of probability densities under consideration, let $k$ be a viscosity function, and let ${\mathcal D}^k$ and $\widetilde{\mathcal D}^k$ be the distanc…

Ruggeri's conjecture. True physical systems are of hyperbolic type.

A real-world fluid has a vanishing second normal-stress difference. Weissenberg's conjecture. All real-world fluids should have vanishing second normal-stress difference. The conje…

Let $y^{k-1}_{\tau}\in W^{1,p}(\Omega;\mathbb{R}^d)$ satisfy $y^{k-1}_{\tau}=y_D$ on $\Gamma_D$, and consider the incremental problem of minimizing … subject to…

Optimality conjecture. For $a\neq 1$, the energy decay rate $t^{-1}$ is optimal.

Consider the system of locally coupled wave equations with localized internal Kelvin–Voigt damping and non-smooth coefficients, for which a polynomial energy decay rate of order…

Spring-path criterion. A viscoelastic model presents solid-like behavior if, for every spring-dashpot fractance of its mechanical analogues, there exists a spring path from one sid…

Consider stationary phase-transitional shock profiles connecting the equilibria $(b_-,a_-)$ and $(b_+,a_+)$ in the phase-transitional viscoelasticity model, with zero shock speed a…

Analytical modulus conjecture. After algebraic manipulation of case studies, analytical moduli can always be formally determined, although they may be exceedingly complex.