Physically Reasonable Solutions to Steady Compressible Navier-Stokes Equations in 2d Exterior Domains with Nonzero Velocity at Infinity

In a previous paper, the present authors studied the asymptotic behaviour of solutions to steady compressible Navier-Stokes equations in barotropic and isothermal regime with sufficiently small external data, in particular, in the whole plane. Here, the same problem is investigated in a two dimensional exterior domain with the prescribed velocity at infinity v_￥ 1 0 v_{\infty}\ne 0 . Similar results as in Dutto and Novotny [DuNo] are found; in particular, it is proved that there exists a unique solution which possesses the similar pointwise decay and the wake structure as the fundamental Oseen tensor.     

π‐Extended Indenofluorenes

A series of π‐extended aromatic indenofluorene (IF) analogues with naphthalene and anthracene cores have been synthesized through acid‐catalyzed intramolecular cyclization. The regioselectivity of the reaction is controlled by a combination of steric and electronic factors and in some cases several possible regioisomers have resulted from the same precursor. The effects of ring connectivity on the optoelectronic properties were investigated by DFT calculations, absorption/emission spectroscopy, cyclic voltammetry, and spectroelectrochemical studies. All regioisomers exhibited a redshift of their absorption/emission bands relative to the parent IF analogues, but the magnitude of this shift and other optoelectronic properties (luminescence quantum yield, etc.) depends on the ring connectivity in a less obvious manner.     

Existence and Uniqueness for a Crystalline Mean Curvature Flow

An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global‐in‐time solution follows via a minimizing movement approach.© 2016 Wiley Periodicals, Inc.     

A Remark on the Smoothness of Bounded Regions Filled with a Steady Compressible and Isentropic Fluid

For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.