Asymptotic Behavior of a Viscous Liquid-Gas Model with Mass-Dependent Viscosity and Vacuum

In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions $n(x,t)$,\$m(x,t)$ when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improves the corresponding result about Navier-Stokes equations in \cite{Zhu}.Comment: 24 page

2D-Delocalized vs Confined Diradicals

Resumen de la comunicación oral seleccionadaDiradicals are beautiful chemical objects where the more basic and intricate aspects of the chemical bonding are revealed.1 Not this being important enough, nowadays, diradical-based substrates are becoming very appealing for new organic electronic applications. We focus here in conjugated organic diradicals formed by competition between non-aromatic quinoidal structures and their canonical aromatic forms. How this quinoidal(closed-shell)-vs-aromatic(open-shell) energetic balance producing the diradical is affected by several situations has been our objective in the last few years.2 Now, we focusses on how the properties of diradicals are influenced when several diradical canonical forms are available in such a way that create a 2D (i.e., bidimensional) electron delocalization surface in which the diradical substructures are in cross-conjugation mode producing the curious effect of diradical confinement.3 Herein, the diradical molecular properties of compound 1 in Figure 1 will be discussed in connection with 2D delocalization, cross-conjugation and surface confinement. 1. Rajca, A., Chem. Rev., 1994, 94, 871; Abe, M., Chem. Rev. 2013, 113, 7011. 2. Zeng, Z.; X. Shi, L.; Chi, C.; Casado, J.; Wu, J. Chem. Soc. Rev. 2015, 44, 6578. 3. Yuan, D.; Huang, D.; Medina Rivero, S.; Carreras, A.; Zhang, C.; Zou, Y.; Jiao, X.; McNeill, C.R.; Zhu, X.; Di, C.; Zhu, D.; Casanova, D.; Casado, J. CHEM, 2019, accepted.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech