In this paper, the non-autonomous dynamical behavior of weakly damped wave equation with a sup-cubic nonlinearity is considered in locally uniform spaces. We first prove the global well-posedness of the Shatah-Struwe solutions, then establish the existence of the H 1 lu (R 3) × L 2 lu (R 3), H 1 ρ (R 3) × L 2 ρ (R 3)-pullback attractor for the Shatah-Struwe solutions process of this equation. The results are based on the recent extension of Strichartz estimates for the bounded domains.

The aim of this paper is to consider the asymptotic dynamics of solutions to 2D MHD equations when the external forces contain some hereditary characteristics. First, we establish, respectively, the well-posedness of strong solutions and weak solutions; then, the process Ũ(⋅,⋅) generated by the weak solutions is constructed in MH2(=H×LH2); and finally, we analyze the long-time behavior of the weak solutions by proving the existence of a compact pullback attractor.

This paper is concerned with a non-autonomous sup-cubic semilinear wave equation in a smooth bounded domain of R 3 , using the introduced weak topology entropy, we obtain an upper bound for the ε-entropy of the uniform attractor for the case where the external forces are not translation-compact.

This study establishes strategies for the science and technology park (STP) operators to develop the support their hosted companies/startups (HCs) need to improve their performance at different stages of maturity. Unlike most of the research concentrated on the STP's viewpoints or used the after-the-fact results to create the policy guidelines for the operators, our paper uses the opposite approach by directly asking the HCs regarding what they need. From our survey results, we have identified two different strategies for improving HCs' performance. A comprehensive internal incubation network is necessary for any startup in a relatively mature development stage but with short settled years. On the other hand, a robust external incubation network is crucial for small-size startups in a low level of development stage but with long-settled years at STPs. We hope that the methodology underpinned in this study could open a new window for future research to better aid HCs in an STP.

This paper aims at the long-time behavior of non-autonomous 2D Navier–Stokes equations with a class of external forces which are [Formula: see text]-valued measures in time. We first establish the well-posedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of [Formula: see text]-entropy for such uniform attractor in the standard energy phase space.