Covalent Organic Polymers with Solid-State Dual-Color Fluorescence Tunable by Ultraviolet Irradiation

An aldol condensation-based strategy is developed for preparing covalent organic polymers (COPs) with strong solution and solid-state dual fluorescence. Moreover, the fluorescence property can be facilely tuned by two ways:...

The Existence of Strong Solution for Generalized Navier-Stokes Equations with p x -Power Law under Dirichlet Boundary Conditions

In this note, in 2D and 3D smooth bounded domain, we show the existence of strong solution for generalized Navier-Stokes equation modeling by p x -power law with Dirichlet boundary condition under the restriction 3 n / n + 2 n + 2 < p x < 2 n + 1 / n − 1 . In particular, if we neglect the convective term, we get a unique strong solution of the problem under the restriction 2 n + 1 / n + 3 < p x < 2 n + 1 / n − 1 , which arises from the nonflatness of domain.

The Stabilization of the Solution of an inverse Problem for the Pseudoparabolic Equation

The asymptotic behavior of the strong solution to the inverse problem on recovering an unknown coefficient k(t) in a pseudoparabolic equation (u + ηMu) t + Mu + k(t)u = f is investigated. The differential operator M of the second order with respect spacial variables is supposed to be elliptic and selfajoint. It is proved that the solution of the inverse problem stabilizes to the solution of the appropriate stationary inverse problem as t → + ∞.

Global Weak Solutions for the Weakly Dissipative Dullin-Gottwald-Holm Equation

In this paper, we are concerned with the existence and uniqueness of global weak solutions for the weakly dissipative Dullin-Gottwald-Holm equation describing the unidirectional propagation of surface waves in shallow water regime: ut − α2uxxt + c0ux + 3uux + γuxxx + λ(u − α2uxx) = α2(2uxuxx + uuxxx).Our main conclusion is that on c0 = − γ/α2 and λ ≥ 0, if the initial data satisfies certain sign conditions, then we show that the equation has corresponding strong solution which exists globally in time, finally we demonstrate the existence and uniqueness of global weak solutions to the equation.