Vanishing viscosity limit of Navier–Stokes Equations in Gevrey class

In this paper, we consider the inviscid limit for the periodic solutions to Navier–Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier–Stokes equation is independent of viscosity, and that the solutions of the Navier–Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover, the convergence rate in Gevrey class is presented. Copyright © 2017 John Wiley & Sons, Ltd.     

Rhodium(III)‐Catalyzed Activation of C?H Bonds and Subsequent Intermolecular Amidation at Room Temperature

Disclosed herein is a Rh^III‐catalyzed chelation‐assisted activation of unreactive C H bonds, thus enabling an intermolecular amidation to provide a practical and step‐economic route to 2‐(pyridin‐2‐yl)ethanamine derivatives. Substrates with other N‐donor groups are also compatible with the amidation. This protocol proceeds at room temperature, has a relatively broad functional‐group tolerance and high selectivity, and demonstrates the potential of rhodium(III) in the promotive functionalization of unreactive C H bonds. A rhodacycle having a SbF₆⁻ counterion was identified as a plausible intermediate.     

Intramolecular Cyclization of 1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in Triflic Acid

1-(ω-Phenylalkyl)-2-(nitromethylene)pyrrolidines in triflic acid undergo a C,O-diprotonation, followed by loss of water, to form conjugated iminium–hydroxynitrilium dications, which react with the tethered phenyl ring by electrophilic aromatic substitution to afford tricyclic iminium compounds as triflate salts. The scope and mechanism of this reaction are discussed.     

Cleavage of Diethyl Chromonyl α-Aminophosponate with Nitrogen and Carbon Nucleophiles: A Synthetic Approach and Biological Evaluations of a Series of Novel Azoles,Azines, and Azepines Containing α-Aminophosphonate and Phosphonate Groups

A convenient synthetic approach leading to a series of novel substituted azoles, azines, and azepines linked to the α-aminophosphonate moiety was achieved. The methodology depends on ring opening and ring closure (RORC) of the chromone ring of diethyl chromonyl α-aminophosphonate 1 via its reaction with nitrogen nucleophiles such as primary amines and 1,2-, 1,3-, and 1,4-bi-nucleophiles in ethanolic sodium ethoxide. Also, treatment of compound 1 with some acyclic and cyclic active methylene compounds under the same reaction conditions afforded interesting novel isolated and fused pyridine systems bearing phosphonate groups at the α-position. The screening of antimicrobial activity for the synthesized compounds indicates that connection of pyrazole, oxazepine, and benzodiazepine rings with α-aminophosphonate moiety exhibited good antimicrobial effects. Also, evaluation of their antioxidant properties shows that the compounds having 1,5-benzoxazepinyl and 1,5-benzodiazepinyl units in combination with α-aminophosphonic diester moiety are the most powerful antioxidant agents.     

K2S2O8-Mediated Difunctionalization of C≡C Bonds in Water: A Simple and Efficient Approach to α,α-Dihaloacetophenones from Phenylacetylenes and NaX

A novel K₂S₂O₈-mediated oxy-1,1-dihalogenation of alkynes with NaX in the presence of water has been developed, affording α,α-dihaloacetophenones in moderate to good yields. The advantages of this reaction are mild reaction conditions, operational simplicity, and use of pure water as reaction medium. A plausible reaction mechanism is proposed on the basis of mechanistic studies.     

Efficient Synthesis of Some New 2,3-Dimethylquinoxaline-1-oxides Using Bis(acetoxy)phenyl-λ 3-iodane as an Oxidant

A series of 2-(arylimino)-3-(hydroxyimino)butanes 3a–g, easily accessed by the condensation of variously substituted anilines 1a–g with biacetyl monoxime 2, were efficiently cyclized to afford 2,3-dimethylquinoxaline-1-oxides 4a–g using bis(acetoxy)phenyl-λ ³-iodane as an oxidant. This methodology utilizes a commercially available and environmental benign oxidant to achieve the title compounds in excellent yields under mild conditions.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]