3 problems

0 votes0 replies0 views
Monotonicity conjecture for blow-up time in damped and supercritical nonlinear Schrödinger equations
Consider the damped cubic Schrödinger equation in dimension two … with $(t,x)\in\mathbb{R}_+\times\mathbb{R}^2$ , initial datum $\psi|_{t=0}=u_0$ , and damping parameter $\delta>0$ .…
Conjectureopenblow-up damped-equations nonlinear-schrodinger-equationsarXiv posted 2 days ago
0 votes0 replies0 views
Global-attractor conjecture for periodic solutions of weakly damped systems
Global-attractor conjecture. When a periodic solution exists, it should serve as a global attractor: trajectories are expected to converge to this unique periodic orbit.
Conjectureopendamped-equations dynamical-systems periodic-solutionsarXiv posted 2 days ago
0 votes0 replies0 views
Eventual nonnegative damping conjecture for scattering
Consider the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential and damping function, under the hypotheses of Theorem 1 in the source, which gives…
Conjectureopendamped-equations nonlinear-schrodinger-equations scatteringarXiv posted 2 days ago

Monotonicity conjecture for blow-up time in damped and supercritical nonlinear Schrödinger equations